Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Wu-Hua Chen, Liangping Cheng, Xiaomei Lu In this paper, the network-based observation and stabilization problems for Lipschitz nonlinear systems under scheduling communication are investigated. It is assumed that the signal transmission between the sensors and the controller or between the controller and the plant is implemented through a wireless network. Moreover, the scheduling of the sensed signal towards the controller is ruled by the Round-Robin (RR) protocol or the i.i.d. stochastic protocol. A general framework for observer-based feedback stabilization is proposed in which the control input is generated by a zero-order device which stores the sampled output of the sample-and-hold Luenberger observer-based controller. The resulting closed-loop system is modeled as a cascaded hybrid system with partial state subject to impulsive perturbation. Sufficient conditions for the existence of sample-and-hold Luenberger observer-based sampled-data controllers are derived by applying separation principle and time-dependent Lyapunov functionals. These conditions allow to design observers and controllers separately. A numerical example is presented to illustrate the effectiveness of the developed methodology.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Yang Li, Hongbin Zhang This paper investigates the dwell time stability and stabilization problems of discrete-time switched positive linear systems (DSPLSs) with interval uncertainties. The dwell time refers to constant dwell time, ranged dwell time and minimum dwell time. At first, some sufficient conditions are presented for the dwell time stability of primal and transpose interval DSPLSs. Meanwhile, the conservatisms of these conditions are compared. Then, equivalent stabilization conditions are presented for interval DSPLSs with dwell time. The controller gain matrices can be computed by solving the convex lifted conditions directly. All the results are given in terms of linear programming (LP). At last, several numerical examples verify the correctness and significance of the results.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Xiaoli Chen, Youguo Wang, Songlin Hu The problem of event-triggered quantized H∞ control of networked control systems (NCSs) under denial-of-service (DoS) jamming attacks is investigated in this paper. Firstly, a new resilient event-triggering transmission scheme is proposed to lighten the load of computing and communications while offsetting the DoS jamming attacks imposed by power-constrained Pulse-Width Modulated (PWM) jammers. Secondly, a new switched system model is established, which characterizes the effects of the event-triggering scheme, quantization and DoS jamming attacks within a unified framework. Thirdly, linear matrix inequality (LMI)-based sufficient conditions for ensuring the exponential stability of the resulting switched system under the DoS jamming attacks are derived by using the piecewise Lyapunov functional method. Moreover, if the obtained LMIs are feasible, the co-design of the event-triggering parameter and the feedback gain matrix can be obtained. Finally, a satellite yaw angle control system is given to verify the effectiveness and feasibility of the developed theoretical results.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Jinghai Shao, Chenggui Yuan This work is concerned with the stability of regime-switching processes under the perturbation of the transition rate matrices From the viewpoint of application, two kinds of perturbations are studied: the size of the transition rate matrix is fixed, and only the values of entries are perturbed; the values of entries and the size of the transition matrix are all perturbed. Moreover, both regular and irregular coefficients of the underlying system are investigated, which clarifies the impact of the regularity of the coefficients on the stability of the underlying system.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Fatima Z. Taousser, Michael Defoort, Mohamed Djemai, Seddik M. Djouadi, Kevin Tomsovic This paper investigates stability for a class of switched nonlinear systems evolving on a non-uniform time domain. The studied class of systems switch between a nonlinear continuous-time and a nonlinear discrete-time subsystem. This problem is formulated using time scale theory where the latter is formed by a union of disjoint intervals with variable lengths and variable gaps. Using Gronwall’s inequality and properties of the time scale exponential function, sufficient conditions are derived to ensure exponential stability. The results can be applied to cases where the continuous-time subsystem or the discrete-time subsystem is not necessarily stable, and the state matrices of each subsystem are not necessarily pairwise commuting. To illustrate the effectiveness of the proposed scheme, the consensus problem for general linear multi-agent systems under intermittent information transmissions is studied under this framework.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Eric Sidorov, Miriam Zacksenhouse Limit cycles occur in a wide range of nonlinear and hybrid systems including dynamic walking. While methods for determining local stability of limit cycles are available, they are relevant only for small perturbations. Characterizing the robustness of limit cycles to larger perturbations is an important, yet mostly open, challenge. Robustness can be characterized by the basin of attraction (BA), but standard techniques for computing BAs are computationally intensive. Here we present an algorithm to estimate inner bounds of BAs of fixed points of polynomial discrete maps. The algorithm is based on a convex optimization problem known as Sum of Squares programming, and results in BA estimates which are expressed as sublevel sets of polynomial Lyapunov functions. The method can be applied to estimate BAs of fixed points of discrete Poincaré Maps and thus the BAs of limit cycles on selected Poincaré sections, as demonstrated on a simple biped walking model under different modes of actuation. For each mode of actuation, the Poincaré map was fitted using a small number of simulations and an inner bound for the BA was estimated. Comparing the BAs achieved by the different modes of actuation demonstrates that the BA of a passive biped model can be enlarged using minimalistic event-driven actuation, and that this relationship is also apparent from the estimated inner bounds of the BAs.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Jiafu Wang, Chuangxia Huang, Lihong Huang The aim of this paper is to deal with the problem of limit cycles for a general planar piecewise linear differential system of saddle–focus type. By using the Liénard-like canonical form with five parameters and dividing the total parameter space into several regions, the number of limit cycles is discussed in detail. In particular, we give parameter regions where there are at least two limit cycles. Moreover, we investigate the existence and stability of exactly two nested limit cycles in some parameter regions.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Dylan Poulsen, Nick Wintz In this paper, we discretize a stochastic linear time-invariant system to a dynamic system on a time scale. We then develop a Kalman filter to estimate the true state for the corresponding system. Here, the measurement-update and time-update equations account for the size of the time step when the time scale is generated randomly. Numerical examples are also provided.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Zbigniew Bartosiewicz Positive uniform exponential stability of positive nonlinear systems on arbitrary time scales with bounded graininess function is studied. It is proved that linearization preserves positivity of systems. Then it is shown that positive uniform exponential stability of the linear approximation of a nonlinear system implies positive uniform exponential stability of the nonlinear system.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): S. Mohanapriya, R. Sakthivel, O.M. Kwon, S. Marshal Anthoni This paper employs an active disturbance rejection technique for a class of singular Markovian jump systems with external disturbances, time-varying delay and unknown nonlinear uncertainty. Based on the improved equivalent-input-disturbance approach, a robust modified repetitive controller is proposed to the considered system to solve the periodic output tracking problem. An appropriate Lyapunov–Krasovskii functional is selected to guarantee the mean-square asymptotic admissibility of the system under study. Moreover, an explicit expression of the proposed controller is presented which has the capability of forcing the system output to exactly track any given periodic reference signal. Finally, the obtained results are validated through simulations by considering a DC motor driving model to demonstrate the effectiveness of the proposed control design technique.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Wei Zhao, Wenwu Yu, Huaipin Zhang In this paper, we propose an event-triggered consensus tracking control for unknown nonlinear multi-agent systems (NMASs) with disturbances by using adaptive dynamic programming (ADP) technique. Considering the disturbances as control inputs, the optimal consensus tracking control problem can be transformed into multi-player zero-sum differential games, where the controllers are designed to minimize the cost functions under the worst-case disturbances. To recover the unknown internal states and control coefficient functions, neural network (NN)-based observers are established. Then, NN-based critics are applied to approximate the value functions and help calculate the optimal control policies and disturbance policies. In order to save the computation resource and reduce the transmission load, the designed observers and controllers are updated only when the designed events are triggered. Stability of the proposed method is demonstrated by Lyapunov analysis for both the continuous and jump dynamics. Meanwhile, we can obtain that the weight estimated errors of the observer NNs, the critic NNs and the local neighbor consensus tracking errors are uniformly ultimately bounded (UUB). Finally, a simulation example is given to illustrate the effectiveness of the proposed approach.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Zhenkun Huang, Jinde Cao, Jiamin Li, Honghua Bin This paper is concerned with quasi-synchronization issue of neural networks which take parameter mismatches and a delayed impulsive controller into account on time scales. Due to the existence of hybrid time domains, there exists novel inherent quasi-synchronization mechanism which will show relationships between mismatching parameters and delayed impulses. Based on calculus of time scales and the direct Lyapunov method, some scale-type criteria to achieve the quasi-synchronization of neural networks under impulsive control are derived. Finally, a numerical simulation is presented to illustrate the effectiveness of theoretical analysis.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Yan Liu, Pinrui Yu, Dianhui Chu, Huan Su Graph-theoretic approach as a new technique is applied to analyze the issue of stationary distribution for stochastic multi-group models (MGMs) with Markovian switching and dispersal. The feature of our model is combining the white noise, the dispersal with Markovian switching, which can model systems in practice reasonably. By constructing a global Lyapunov function for stochastic MGMs with Markovian switching and dispersal, sufficient criteria, which guarantee the existence of a stationary distribution, are presented via the combination of the graph theory, the Lyapunov method and the M-matrix method. Moreover, stochastic coupled oscillators with Markovian switching and dispersal are presented as a practical application to illustrate our results in the end.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Yuanyuan Zhang, Renfu Li, Xiaoming Huo This paper is concerned with the exponential stability of numerical solutions for neutral stochastic differential delay equations (NSDDEs) with Markovian switching (or hybrid NSDDEs). It is known that Markov chain can work as a stabilizing factor, that is, when some subsystems are stable and others are unstable, the overall system can be stable. In this paper, such property is called switching-dominated stability, and we prove that the switching-dominated stability can be recovered in the stability of numerical solutions based on the switched Lyapunov function method. Firstly, a fundamental stability criterion is established for the numerical solutions. Then under a linear growth condition, we show that the Euler–Maruyama (EM) method can share the mean square exponential stability of the exact solution. When the linear growth condition is defied, but a one-sided Lipschitz condition is satisfied, we show that the backward EM (BEM) method can reproduce the mean square exponential stability of the exact solution. Numerical experiments are carried out to confirm the theoretical results.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Yuechao Ma, Yangfan Liu This paper investigates the finite-time H∞ control problem for singular Markovian jump system with actuator fault through the sliding mode control approach. Based on the observer, the augment system can be constructed with time-varying delays and actuator failure. Continuous actuator failure model is considered in this paper. Next, a sliding surface is considered under which sufficient conditions are given to make sure the augment system is singular stochastic H∞ finite-time bounded. And the sliding mode control law is synthesized to guarantee the reachability of the sliding surface in a short time interval. The state feedback controller gain matrices and observer gain matrices are obtained by solving the relevant linear matrix inequalities. Decoupling method has been adopted for the coupled variables. Finally, simulation examples illustrate the validity of the proposed method.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Guowei Yang, Binghua Kao, Ju H. Park, Yonggui Kao We work on the investigation of the H∞ performance for uncertain stochastic singular Markovian jump systems with both nonlinear external disturbance and general unknown transition rates (TRs) in this paper. There exist uncertainties in both parameters and TRs. Every transition rate could be totally unavailable or only its estimated value is available. With a generalized H∞ disturbance attenuation level γ, some robust controllers are designed such that the delayed singular Markovian jump system is stochastically admissible. The novel controllers designed in this paper consist of an adaptive controller and a linear controller. Moreover, some sufficient linear matrices inequalities (LMIs) conditions are provided according to Lyapunov stability theory and Itoˆ’s differential formula. Finally, an example is presented to demonstrate our main results.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): L.G. Moreira, S. Tarbouriech, A. Seuret, J.M. Gomes da Silva Jr. This paper presents an observer-based event-triggered strategy for linear systems subject to input cone-bounded nonlinearities. Both the emulation and co-design problems are addressed. Considering a Lyapunov approach and the cone-bound property of the input nonlinearity, sufficient conditions based on linear matrix inequalities are derived to ensure regional or global asymptotic stability of the origin of the closed-loop system. These conditions are incorporated into convex optimization problems to optimally determine the event generator parameters and the controller gain (in the co-design case) aiming at reducing the number of control updates with respect to periodic implementations for a prescribed observer gain. The event-triggering strategy considers a dwell time to cope with Zeno behaviors. Numerical examples, considering systems with quantized logarithmic inputs and saturating inputs, illustrate the potentialities of the approach.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Biao Zeng, Zhenhai Liu The goal of this paper is to provide systematic approaches to study the feedback control systems governed by impulsive evolution equations in separable reflexive Banach spaces. We firstly give some existence results of mild solutions for the equations by applying the Banach’s fixed point theorem and the Leray–Schauder alternative fixed point theorem with Lipschitz conditions and different types of boundedness conditions. Then, by using the Filippove theorem and the Cesari property, a new set of sufficient assumptions are formulated to guarantee the existence results of feasible pairs for the feedback control systems. Finally, we apply our main result to obtain a controllability result for impulsive evolution equations and two existence results for a class of impulsive differential variational inequalities and impulsive Clarke’s subdifferential inclusions.

Abstract: Publication date: August 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 33Author(s): Ying Zhao, Jun Zhao, Jun Fu This study concentrates on the problem of bumpless transfer control for a category of switched positive linear systems with L1-gain property. The objective is to reduce the control bumps at switching instants and to maintain the L1-gain property as well. For a system in this category with pre-designed controllers, a controller gain interpolation technique is employed to realize the bumpless transfer control. Under the bumpless transfer controllers, the system can satisfy the L1-gain property for any switching rules with a dwell time restraint. For the general case, that is, the controllers are to be designed, the bumpless transfer performance is described by a magnitude constraint on the control signal. By co-design of the controllers and switching scheme, we solve the issue of bumpless transfer control for the system with L1-gain property, even if the problem of the subsystems is unsolvable. Also, a sufficient condition ensuring the bumpless transfer performance and the L1-gain property is obtained. Finally, via controlling a turbofan model, we illustrate the effectiveness of the presented control strategies.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Dong Zhao, Hamid Reza Karimi, Rathinasamy Sakthivel, Yueyang Li The non-fragile fault-tolerant control for a class of nonlinear Markovian jump systems with intermittent multiple actuator faults is addressed in this study. The nonlinearity in the considered system is assumed to satisfy sector constraint. Multiple Markov chains are introduced to model the multiple intermittent actuator faults, which is in a multiplicative form. To ensure the fault tolerance of the closed-loop system in the presence of potential controller perturbation, a new non-fragile fault-tolerant controller is designed, which can stabilize the resulting closed-loop system and further satisfy a prescribed performance index. After appropriately synthesizing the fault model that dominated by multiple Markov chains and the underlying nonlinear Markovian jump system, a set of sufficient conditions for the considered problem focusing on the controller design is derived with both known and partially known transition probabilities, where the controller can be determined via a convex optimization procedure. An example is given to illustrate the effectiveness of the proposed controller.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Junfeng Zhang, Tarek Raïssi This paper investigates the saturation control for a class of switched nonlinear systems, where the nonlinearity function is restricted in a sector. The proposed approach is based on the theory of positive systems and a criterion is addressed to ensure the positivity property of the considered systems. The system states starting from a cone will remain in another cone. Under an average dwell time condition, a control design methodology is established in terms of linear programming. It is shown in this paper that the proposed approach can be applied for positive systems and also for a general class of nonlinear systems. Then, the saturation control synthesis of switched nonlinear systems with exogenous disturbances is addressed. Under the designed saturation controller, the states of each subsystem start from a cone and remain within it. Thus, the states of the switched systems start from a cone containing the origin and remain in another cone. Finally, the proposed methodology is applied to a nonlinear control system.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Pengfei Wang, Mengxin Wang, Huan Su This paper aims to investigate the stability of random coupled systems on networks with Markovian switching (RCSNM), which is driven by general noise instead of white noise. By using Lyapunov method, graph-theoretical technique as well as stochastic analysis technique, some novel sufficient criteria are derived to ensure the global asymptotical stability in probability and exponential stability in pth moment for RCSNM, respectively. It is worth noting that the two kinds of stability for RCSNM are studied for the first time. Based on the theoretical results, the stability of a class of coupled oscillators with Markovian switching and general noise is investigated. Numerical simulations are also included to show the effectiveness and feasibility of the derived results.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Dan Yang, Xiaodi Li, Jianlong Qiu This paper investigates the problem of output tracking control for a class of delayed switched linear systems via state-dependent switching and dynamic output feedback control. A state-dependent switching rule and the switching regions are proposed. Then the stability and tracking performance analysis are proposed based on single Lyapunov function technique, respectively. The design problem of dynamic output feedback controllers can be solved efficiently by using linear matrix inequalities (LMIs) toolbox. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Trang Bui, Xiang Cheng, Zhuo Jin, George Yin This work develops an approximation procedure for a class of non-zero-sum stochastic differential investment and reinsurance games between two insurance companies. Both proportional reinsurance and excess-of loss reinsurance policies are considered. We develop numerical algorithms to obtain the approximation to the Nash equilibrium by adopting the Markov chain approximation methodology. We establish the convergence of the approximation sequences and the approximation to the value functions. Numerical examples are presented to illustrate the applicability of the algorithms.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Yukang Cui, Jun Shen, Guang-Zhong Cao This paper considers the problems of reachable set estimation and synthesis of delta operator systems under bounded peak disturbances. A basic reachable set estimation tool for delta operator systems is developed, which can be reduced to the z-domain or s-domain forms when sampling period is 1 or tends to 0. Through the obtained generalized criterion of reachable set, the ellipsoidal reachable set estimation condition of delta operator systems is proposed. Moreover, the state-feedback controller design problem for delta operator systems is investigated. The intention of the controller is to bound the closed-loop system to a given ellipsoid or to make the reachable set of system trajectory as small as possible. Finally, the effectiveness of the obtained results are illustrated by several numerical examples.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Shixian Luo, Feiqi Deng This paper studies the pth moment and almost sure stabilization of a class of nonlinear hybrid stochastic systems with input delays in both the switching signal and the state. By using Lyapunov functional approach, sufficient conditions are established in terms of sizes of the delays ensuring the pth moment exponential stability of the systems. By developing a composite mode-dependent Lyapunov function approach, we derive novel almost sure exponential stability criteria for a delay-free hybrid stochastic system without imposing the stability condition on the subsystems. We further prove that the almost sure stability property of the hybrid system with delayed feedback controller is preserved as long as the corresponding delay-free system is almost sure exponential stabilization and the delays are small enough. Numerical examples demonstrate the theoretical results.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Sung Jin Yoo This paper addresses a distributed low-complexity design problem for ensuring preassigned fault-tolerant consensus tracking quality of uncertain switched nonlinear pure-feedback multi-agent systems under arbitrary and asynchronous switching. Switched non-affine nonlinearities and unexpected nonlinear and actuator faults of each system are assumed to be unknown. Compared with existing results in the literature, the main contribution of this paper is to provide a simplified robust control strategy to deal with asynchronously switched nonlinearities and faults among systems in the consensus tracking field. Using nonlinearly transformed error surfaces and the common Lyapunov function method, a common robust consensus tracking design strategy is established to ensure the preassigned fault-tolerant consensus tracking performance and the system reliability on the switched faults, without using any adaptive fault compensation techniques based on neural networks or fuzzy logic systems. It is shown that the distributed consensus tracking errors remain within preselected bounds even at switching and fault occurrence instants and finally converge to a preselected neighborhood of the origin.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Martin Bohner, Sabrina Streipert, Delfim F.M. Torres We investigate an epidemic model based on Bailey’s continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner’s approach. If the coefficients are constant, both solution methods yield the same result. After a brief introduction to time scales, we formulate the SIR (susceptible–infected–removed) model in the general time domain and derive its solution. In the discrete case, this provides the solution to a new discrete epidemic system, which exhibits the same behavior as the continuous model. The last part is dedicated to the analysis of the limiting behavior of susceptible, infected, and removed, which contains biological relevance.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Yacun Guan, Hao Yang, Bin Jiang This paper addresses the fault tolerant control (FTC) problem for switched parabolic systems with process and boundary faults, described by partial differential equation (PDE). The boundary feedback controller is designed to guarantee the exponential stability of the systems. Both the accumulative and dissipative characteristics of faults are considered, respectively. Constructing the comparative system and using Lyapunov method, the non-switched parabolic systems are exponentially stable. The new result is further extended to the switched parabolic systems where the boundary controller in each mode and the switching law are designed comprehensively. It shows that the FTC goal can be achieved even if only some faulty modes are stabilizable. A heat propagation control of semiconductor power chips example is taken to illustrate the efficiency of obtained theoretical results.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Zhu Wang, Haoran An, Xionglin Luo Switch detection and robust identification for slowly switched Hammerstein systems are considered in this paper. The switching law is slow, arbitrary and cannot be observed online. A two-identifier-based switch detection scheme is proposed, in order to achieve fast adaptability and robustness of parameter estimation. Specifically, at first, a recursive identification method based on long-horizon iteration is exploited under impulsive noise, and its convergence for time-invariant systems is verified. Secondly, to follow the changes of real processes, a forgetting factor is introduced, and two recursive identifiers with different horizon lengths are developed. Identifier (I) with the long horizon length can resist the influence of outliers, and Identifier (II) is responsible for process rapid reactions. Then, the estimated difference between two identifiers is analyzed to distinguish possible switching points from impulsive noise. Consequently, the two-identifier-based switch detection scheme is formed. Finally, a simulation example demonstrates the effectiveness of the proposed scheme.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Héctor Ríos, Laurentiu Hetel, Denis Efimov This paper deals with the sampled-data control problem based on state estimation for uncertain linear sampled-data systems. It is possible to show that the sampled-data control problem based on state estimation may be related with the conditions for the exponential stability of impulsive systems. Thus, a vector Lyapunov function-based approach, derived by means of a 2D time domain equivalence, is used for obtaining stability conditions of an impulsive system, and then, a solution to the observer-based control design problem is derived and expressed in terms of linear matrix inequalities. Some examples illustrate the feasibility of the proposed approach.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Dorota Mozyrska, Delfim F.M. Torres, Małgorzata Wyrwas Caputo–Fabrizio fractional delta derivatives on an arbitrary time scale are presented. When the time scale is chosen to be the set of real numbers, then the Caputo–Fabrizio fractional derivative is recovered. For isolated or partly continuous and partly discrete, i.e., hybrid time scales, one gets new fractional operators. We concentrate on the behavior of solutions to initial value problems with the Caputo–Fabrizio fractional delta derivative on an arbitrary time scale. In particular, the exponential stability of linear systems is studied. A necessary and sufficient condition for the exponential stability of linear systems with the Caputo–Fabrizio fractional delta derivative on time scales is presented. By considering a suitable fractional dynamic equation and the Laplace transform on time scales, we also propose a proper definition of Caputo–Fabrizio fractional integral on time scales. Finally, by using the Banach fixed point theorem, we prove existence and uniqueness of solution to a nonlinear initial value problem with the Caputo–Fabrizio fractional delta derivative on time scales.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Martin Bohner, Veysel Fuat Hatipoğlu In this paper, basic and more realistic dynamic cobweb models are developed in terms of conformable fractional derivatives. The general solutions and stability criteria for the proposed models are given. Moreover, the developed models are illustrated with examples on several time scales.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Yan Zheng, Yaonan Wang In this paper, the l1 filtering problem for positive switched time-delay systems is investigated. An improved delay-dependent MADT that takes delay-independent MADT switching as a special case is provided, and a mode-dependent and time-dependent linear copositive Lyapunov functional is presented to establish the exponential stability with the weighted l1 performance of the filtering error system under the improved MADT. Both full-order and reduced-order filters are designed for the concerned system, and the gains of the filters can be obtained by solving a set of linear programming. Two numerical examples are presented to demonstrate the effectiveness of the proposed theories.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Jorge Júlvez, Stephen G. Oliver A number of artificial and natural systems can be modeled as hybrid models in which continuous and discrete variables interact. Such hybrid models are usually challenging to analyze and control due to the computational complexity associated with existing methods. In this paper, the novel modeling formalism of Guarded Flexible Nets (GFNs) is proposed for the modeling, analysis and control of hybrid system. A GFN consists of an event net that determines how the state changes as processes execute, and an intensity net that determines the speeds of the processes. In a GFN, the continuous state is given by the value of its state variables, and the discrete state is given by the region within which such variables lie. GFNs are shown to possess a high modeling power while offering appealing analysis and control possibilities.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Pengfei Wang, Jiqiang Feng, Huan Su This paper concerns the stabilization problem of stochastic delayed networks with Markovian switching and hybrid coupling (SDNMH) via aperiodically intermittent control. Compared with the existing works on hybrid coupling, the hybrid coupling in this paper can be nonlinear, which is more general. By establishing a new differential inequality on delayed dynamical systems with Markovian switching, the stabilization problem of SDNMH via aperiodically intermittent control is studied. By means of Lyapunov method and graph-theoretic technique, two kinds of sufficient criteria are given. The derived results are closely related to the topology structure of the underlying network, the transition rate of Markov chain, the maximum proportion of rest time and the control gain. Finally, the theoretical results are tested by a class of coupled oscillators networks with Markovian switching and hybrid coupling.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): A.A. Martynyuk, I.M. Stamova In the first part of the paper a family of hybrid systems with aftereffect is considered. For such equations, some results of the analysis of a set of trajectories based on matrix-valued functions defined on the product of spaces are given. In the second part of the paper, for the first time, uncertain sets of equations under impulsive perturbations are investigated. Estimates for the distance between extremal sets of trajectories are derived for the systems under consideration. In addition, conditions for the global existence of the sets of solutions regularized with respect to the parameter of uncertainty are proved.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Yaowei Sun, Jun Zhao, Georgi M. Dimirovski In this paper, the adaptive stabilization issue for a class of state-constrained high-order switched nonlinear systems is concerned, where all subsystems are allowed to be unstabilizable. A novel adaptive control scheme is established by exploiting the effective coupling of the technique of adding a power integrator and the method of multiple barrier Lyapunov functions. Explicitly, a group of adaptive controllers and a proper switching law are designed to asymptotically regulate the states of the resulting closed-loop system in a domain and meanwhile guarantee that the violation of the constraints does not happen. Contrary to a common update law constructed for all subsystems in the literature, different update laws for individual subsystems are designed separately to reduce the conservativeness. Moreover, at the switching instants, the connection of two adjacent barrier Lyapunov functions is not be required and even a certain amount of grow is also allowed. Finally, a simulation example is performed to further illustrate the effectiveness of the provided control strategy.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Kai Wang, Yanling Zhu In this paper, a stochastic Gilpin–Ayala population model with regime switching and white noise is considered. All parameters are influenced by stochastic perturbations. The existence of global positive solution, asymptotic stability in probability, pth moment exponential stability, extinction, weak persistence, stochastic permanence and stationary distribution of the model are investigated, which generalize some results in the literatures. Moreover, the conditions presented for the stochastic permanence and the existence of stationary distribution improve the previous results.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Guobao Liu, Ju H. Park, Shengyuan Xu, Guangming Zhuang This paper investigates the problem of non-fragile H∞ fault detection filtering for a class of uncertain time-varying-delay singular Markovian jump systems (SMJSs). Linear fractional parameter uncertainties are considered and the designed filter is supposed to contain gain variations. The main objective is to design a mode-dependent non-fragile fault detection filter to guarantee the fault detection system to be stochastically admissible with an H∞ performance index for all admissible uncertainties. First, by constructing a novel mode-dependent stochastic Lyapunov–Krasovskii functional and employing integral inequality approach, sufficient delay-dependent conditions on stochastic admissibility and H∞ performance analysis for the fault detection system are presented in terms of linear matrix inequalities (LMIs). Then, the existence conditions of the desired fault detection filter and the explicit expressions for calculating the filter parameters are established. Finally, a numerical example and a DC motor are employed to show that our methods are effective.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Bacem Ben Nasser, Khaled Boukerrioua, Michael Defoort, Mohamed Djemai, Mohamed Ali Hammami, Taous-Meriem Laleg-Kirati This paper investigates the exponential stability and h-stability problems of some classes of nonlinear systems. First, we analyze the global uniform exponential stability for a class of integro-differential equations on time scales. We also derive some sufficient conditions for stability using an integral inequality approach. Then, we give an analysis of the h-stability of some classes of linear systems under Lipschitz-type disturbances. To this end, some h-stability criteria are established. Finally, numerical examples are proposed to illustrate the stability concepts.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Peng Wang, Jun Zhao In this paper, we are devoted to investigating dissipativity for a class of positive switched systems by exploiting multiple linear copositive storage functions and multiple linear supply rates. A novel concept of dissipativity is presented, which depicts the overall dissipativity property of positive switched systems without the requirement of the classic dissipativity property of each positive subsystem. A sufficient condition ensuring dissipativity for positive switched systems is given under a designed switching signal. Meanwhile, L1 gain and stability are also get based on dissipativity. Dissipativity and positivity are shown to be maintained under positive feedback interconnection, and a small-gain property is also given. All presented conditions are formulated as a linear programming problem. Two examples are provided to illustrate the effectiveness of the main results.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Wenqian Xie, Hong Zhu, Shouming Zhong, Jun Cheng, Kaibo Shi This paper addresses the problem of extended dissipativity-based resilient state estimation for discrete-time switched neural networks in the presence of unreliable links. To overcome the difficulty of random fluctuation and communication constraints, a novel and highly flexible form of estimator is designed by considering random uncertainty, signal quantization and data packet dropout phenomena simultaneously. The considered mode-dependent average dwell time (MDADT) switching law is shown to be more general than the traditional ADT for permitting each subsystem to has its own average dwell time. By constructing the MD Lyapunov–Krasovaskii functional (LKF), sufficient conditions are given to ensure the exponential mean-square stability and extended stochastic dissipativity of the augmented system and an explicit expression of the desired estimator is presented. Finally, a example with two cases is provide to illustrate the feasibility and effectiveness of the developed theoretical results.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Andrea Aparicio, Leonid Fridman, Denis Efimov The stabilization problem for switched systems in which switchings occur on the axes of its state coordinates is considered. It is shown that a linear feedback, or a combination of linear feedback and a switching law, can be designed such that the closed-loop is stable, and has the input-to-state property, allowing to guarantee robustness against matched and unmatched perturbations. The conditions of stability are expressed in the form of linear matrix inequalities. The results are illustrated by numerical simulations.

Abstract: Publication date: May 2019Source: Nonlinear Analysis: Hybrid Systems, Volume 32Author(s): Xianfu Zhang, Xiaodong Lu, Zhi Liu In this paper, asymptotic stability problems of nonlinear delay impulsive systems on time scales are considered based on the Razumikhin and Krasovskii methods. First, a Krasovskii-type theorem is provided for uniform asymptotic stability and uniform exponential stability of delay impulsive systems on time scales. It is shown that this Krasovskii stability criterion does not require the time derivative of the Lyapunov functional to be necessarily nonpositive on each impulsive interval. Second, asymptotic stability problems of delay impulsive systems on time scales is investigated based on the Razumikhin approach. The advantage of this method is that the length of each impulse interval does not depend on the time delay, which results in the fact that the state trajectory may not decrease instantly and sharply at each impulsive point. Moreover, the idea of this paper provides a unified approach to study continuous system and its discrete counterpart simultaneously. An example is given for illustrating the effectiveness of the proposed results.

Abstract: Publication date: Available online 15 February 2019Source: Nonlinear Analysis: Hybrid SystemsAuthor(s): Guopin Liu, Changchun Hua, Xinping Guan This paper considers the stabilization problem for a class of switched neutral systems under asynchronous switching. A cooperative stabilization approach is presented, which means that controllers and switching signals are designed cooperatively to stabilize the switched system. Based on the Lyapunov–Krasovskii functional approach, a sufficient condition is provided to guarantee the global asymptotical stability of the switched neutral systems. Meanwhile, the controller gain is obtained by solving the established linear matrix inequalities (LMIs). The proposed approach allows the Lyapunov-like function to increase not only at the running time in mode-identifying process but also in normal-working period with matched controller. Thus, switched systems, which contain unstable and uncontrollable subsystems, can be stabilized by the proposed scheme. A numerical example further demonstrates the validity of the developed results.

Abstract: Publication date: Available online 15 February 2007Source: Nonlinear Analysis: Hybrid SystemsAuthor(s): V. Laksmikantham This article has been removed, consistent with Elsevier Policy on Article Withdrawal. Please see http://www.elsevier.com/locate/withdrawalpolicy The Publisher apologizes for any inconvenience this may cause.