In this paper, observers are synthesized for switched linear systems, resulting in switched observers including state jumps. The synthesis problem is formulated as a linear matrix inequality problem. By using multiple Lyapunov functions, a switched state jump observer is designed for a broader class of switched systems than earlier proposed in the literature. Copyright c © 2005 IFAC

The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving these problems in a number of diverse communities , and to review some problems that remain open. An important contribution of our work is to bring to...

Stability of an interconnected system consisting of two switched systems is investigated in the scenario where in both switched systems theremay exist some subsystems that are not input-to-state stable (nonISS). We show that, providing the switching signals neither switch too frequently nor activate non-ISS subsystems for too long, a small-gain theorem can be used to conclude global asymptotic ...

In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an output feedback bounded controller and a predictive controller for each subsystem using high-order differential state observers and Lyapunov functions, to derive a suitable switched la...

It is well known that the bilinear transform, or first order diagonal Padé approximation to the matrix exponential, preserves quadratic Lyapunov functions between continuous-time and corresponding discrete-time linear time invariant (LTI) systems, regardless of the sampling time. It is also well known that this mapping preserves common quadratic Lyapunov functions between continuous-time and di...

This paper develops hybrid control strategies for stabilizing a class of nonlinear systems. Common Lyapunov functions and switched Lyapunov functions are used to establish easily verifiable criteria for the stabilizability of weakly nonlinear systems under switched and impulsive control. Three types of controller switching rules are studied: time-dependent (synchronous), statedependent (asynchr...

This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related t...

In a companion paper [Q. Hui, W.M. Haddad, Semistability of switched dynamical systems. Part I: Linear system theory, Non-linear Anal. Hybrid Syst. 3 (3) (2009) 343–353] semistability and uniform semistability results for switched linear systems were developed. In this paper we develop semistability analysis results for non-linear switched systems. Semistability is the property whereby the solu...

In this paper, we introduce some analysis tools for switched and hybrid systems. We first present work on stability analysis. We introduce multiple Lyapunov functions as a tool for analyzing Lyapunov stability and use iterated function systems (IFS) theory as a tool for Lagrange stability. We also discuss the case where the switched systems are indexed by an arbitrary compact set. Finally, we e...