The stability properties of linear switched systems consisting of both Hurwitz stable and unstable subsystems are investigated by using piecewise Lyapunov functions incorporated with an average dwell time approach. It is shown that if the average dwell time is chosen sufficiently large and the total activation time ratio between Hurwitz stable and unstable subsystems is not smaller than a speci...

The hybrid dynamics of the genetic regulatory networks (GRNs) have attracted much research attention in recent years. This paper is concerned with the stability analysis of piecewise GRNs. Depending on whether the state partitions and mode transitions are known or unknown as a priori, the proposed networks are divided into two categories, i.e., switched GRNs and hybrid GRNs. It is shown that, b...

In this report the ray-gridding approach, a new numerical technique for the stability analysis of linear switched systems is presented. It is based on uniform partitions of the state-space in terms of ray directions which allow refinable families of polytopes of adjustable complexity to be examined for invariance. In this framework the existence of a polyhedral Lyapunov function that is common ...

In this paper we show that certain piecewiselinear Lyapunov functions are preserved for LTI systems under Padé approximations. In particular, we present a simple method to find a piecewise-linear Lyapunov function that is so preserved under the Padé discretization of any order and sampling time. This result may be of interest in the discretisation of switched linear systems for both simulation ...

In this paper, a new class of hybrid impulsive and switching models are introduced. Using switched Lyapunov functions, some new general criteria for exponential stability and asymptotic stability of hybrid impulsive and switched nonlinear systems are established. Further more, a new hybrid impulsive and switching control strategy for the nonlinear systems is developed to improve the system perf...

This paper studies time-delayed switched systems that include both stable and unstable modes. By using multiple Lyapunov functions technique and a dwell time approach, several criteria on exponential stability for both linear and nonlinear systems are established. It is shown that by suitably controlling the switching between the stable and unstable modes exponential stabilization of the switch...

In this paper the discretization of switched and non-switched linear positive systems using Padé approximations is considered. We show: 1) diagonal Padé approximations preserve both linear and quadratic co-positive Lyapunov functions; 2) positivity need not be preserved even for arbitrarily small sampling time for certain Padé approximations. Sufficient conditions on the Padé approximations are...

Abstract The backstepping method is applied to a certain class of switched nonlinear systems to design state feedback controllers and a switching law based on multi-Lyapunov functions. The state feedback controllers and the switching law that can stabilize the system are developed. The switched nonlinear systems with uncertainties can be stabilized robustly by using the proposed method. Finally...

This paper deals with the problem of robust H∞ control for a class of uncertain switched nonlinear systems via the multiple Lyapunov functions approach. Based on the explicit construction of Lyapunov functions, which avoids solving the Hamilton-Jacobi-Isaacs (HJI) inequalities, a condition for the solvability of the robust H∞ control problem and design of both switching laws and controllers is ...