Jie Lian

Observer Design for Switched Recurrent Neural Networks: An Average Dwell Time Approach

This paper is concerned with the problem of observer design for switched recurrent neural networks with time-varying delay. The attention is focused on designing the full-order observers that guarantee the global exponential stability of the error dynamic system. Based on the average dwell time approach and the free-weighting matrix technique, delay-dependent sufficient conditions are developed for the solvability of such problem and formulated as linear matrix inequalities. The error-state decay estimate is also given. Then, the stability analysis problem for the switched recurrent neural networks can be covered as a special case of our results. Finally, four illustrative examples are provided to demonstrate the effectiveness and the superiority of the proposed methods.

Passivity and Passification for a Class of Uncertain Switched Stochastic Time-Delay Systems

This paper is concerned with the problems of passivity and passification for a class of uncertain switched systems subject to stochastic disturbance and time-varying delay. The passivity property is adopted to analyze the influence of the external disturbance on such systems to achieve prescribed attenuation levels. Based on average dwell time approach, free-weighting matrix method, and Jensens integral inequality, delay-dependent sufficient conditions are obtained in terms of linear matrix inequalities, which ensure the uncertain switched stochastic time-delay system to be robustly mean-square exponentially stable and stochastically passive. Then, the switched passive controllers are synthesized by linearization techniques. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

Passivity of Switched Recurrent Neural Networks With Time-Varying Delays

This paper is concerned with the passivity analysis for switched neural networks subject to stochastic disturbances and time-varying delays. First, using the multiple Lyapunov functions method, a state-dependent switching law is designed to present a stochastic passivity condition. Second, a hysteresis switching law involving both the current state and the previous value of the switching signal are presented to avoid chattering resulted from the state-dependent switching. Third, based on the average dwell-time approach, a class of switching signals is determined to guarantee the switched neural network stochastically passive. Finally, three numerical examples are provided to illustrate the characteristics of three proposed switching laws.

Adaptive Variable Structure Control for Uncertain Switched Delay Systems

This paper investigates the robust H∞ control problem for a class of uncertain switched delay systems with parameter uncertainties, unknown nonlinear perturbations, and external disturbance. Based on the multiple Lyapunov functions method, a sufficient condition for the solvability of the robust H∞ control problem is derived by employing a hysteresis switching law and variable structure controllers. When the upper bounds of the nonlinear perturbations are unknown, an adaptive variable structure control strategy is developed. The use of the adaptive technique is to adapt the unknown upper bounds of the nonlinear disturbances so that the objective of asymptotic stabilization with an H∞-norm bound is achieved under the hysteresis switching law. A numerical example illustrates the effectiveness of the proposed design methods.

Exponential stabilization of singularly perturbed switched systems subject to actuator saturation

This paper considers the problem of exponential stabilization for a class of singularly perturbed switched systems subject to actuator saturation. A time-dependent switching law is designed to obtain the exponential stabilization conditions of the switched systems with unstabilizable subsystems. Based on the multiple Lyapunov functions method depending on singular perturbation parameters, a domain of attraction is constructed. Furthermore, in order to maximize an estimate of the domain of attraction, convex optimization problems are formulated. Finally, a numerical example is presented in order to illustrate the effectiveness of the established results.

Robust stability for switched positive systems with D-perturbation and time-varying delay

This paper is focused on studying the robust stability of switched positive systems with D-perturbation and time-varying delay. All subsystems are considered to be unstable. Based on the partition of state space on the nonnegative orthant, sufficient conditions in terms of linear programming are obtained to guarantee such system to be asymptotically stable. The hysteresis switching laws are designed to prevent chattering behavior via the single copositive Lyapunov function and multiple copositive Lyapunov functions approaches, respectively. Two illustrative examples concerned with price model of goods are provided to display the effectiveness of the obtained results.

Distributed containment control of multi-agent systems without dynamic observers of leaders

This paper investigates the distributed containment control problem for multi-agent systems with general linear dynamics under a directed graph. A new observer based on the relative outputs of neighboring agents is developed to estimate the relative states of neighbors which avoid designing the observer for the leaders in the existing literature. A matrix transformation is introduced to eliminate the coupling terms resulting from the simultaneous design of the observer and the controller gains. Then a sufficient condition on the existence of the observer-based controllers is presented in terms of strict linear matrix inequalities. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed design method.

Sliding mode control for switched nonlinear systems under asynchronous switching.

In this paper, an integral sliding mode control approach is employed to analyze the mean-square exponential stability for a class of uncertain switched nonlinear stochastic systems under asynchronous switching signals. Firstly, an integral sliding surface is designed and a sufficient condition for its existence are presented to guarantee the mean-square exponential stability of switched systems in the sliding motion. Then variable controllers are designed such that switched systems remain in the sliding motion from the initial time instant. Due to the asynchronous switching between system modes and the corresponding controllers, the results presented allow the closed-loop systems to be unstable in the mismatched periods. Finally, a numerical example is presented to illustrate the effectiveness of the proposed results.

Stability of switched Hopfield neural networks with time-varying delay

This paper considers the asymptotic stability problem for switched Hopfield neural networks with time-varying delay under hysteretic switching rule. The parameter uncertainties are considered and assumed to be norm bounded. Single Lyapunov function method is used to analyze the stability property and design the hysteretic switching rule, which is designed according to current state and the previous value of switched signal. Sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the stability of the system. An example illustrates the effectiveness of the proposed theory.

Adaptive output tracking of switched nonlinear systems with unmodeled dynamics

This paper is concerned with the problem of output feedback adaptive control for switched systems with unmodeled dynamics and relative degree p. Firstly, for the former p states, based on the local filters, an adaptive controller is designed by using a backstepping recursive design method and a common coordinate transformation for all subsystems. Second, a common Lyapunov function is constructed to establish the boundedness of all signals in the resulting closed-loop switched systems under arbitrary switching signals. Finally, it is shown that a system output can track the desired trajectory.