In this paper, we consider linear switched systems ẋ(t) = Au(t)x(t), x ∈ R, u ∈ U , and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching (UAS for short). We first prove that, given a UAS system, it is always possible to build a common polynomial Lyapunov function. Then our main result is that the degree of that common polynomial Lyapunov f...

This paper addresses the stability problem of a class of nonlinear switched systems with partitioned state-space and state-dependent switching. In lieu of the Carathéodory solutions, the general Filippov solutions are considered. This encapsulates solutions with infinite switching in finite time. Based on the theory of differential inclusions, a Lyapunov stability theorem is brought forward. Th...

This paper is concerned with the existence of a linear copositive Lyapunov function(LCLF) for a special class of switched positive linear systems(SPLSs) composed of continuousand discrete-time subsystems. Firstly, by using system matrices, we construct a special kind of matrices in appropriate manner. Secondly, our results reveal that the Hurwitz stability of these matrices is equivalent to the...

In this paper, the problems of control and stabilization of switched nonlinear cascade systems is investigated. The so called simultaneous domination limitation (SDL) is introduced in previous works to assure the existence of a common quadratic Lyapunov function (CQLF) for switched nonlinear cascade systems. According to this idea, if all subsystems of a switched system satisfy the SDL, a CQLF ...

In this paper, the problems of state and fault estimation are addressed for a class of switched descriptor systems subject to Lipschitz nonlinearities and unknown inputs (UI). The UI appear both on the dynamic and on the measurement equations. Two problems are addressed by L2-gain minimization with the use of switched Lyapunov functions and formulated by LMI. First, a functional observer for sw...

In this paper we extend LaSalle’s Invariance Principle to certain classes of switched linear systems. In particular we illustrated how to prove asymptotic stability using multiple Lyapunov functions whose Lie derivatives are only negative semi-definite.

This paper addresses two strategies for stabilization of continuous time linear switched system. The first one, is of open loop nature (trajectory independent) and is based on the determination of a minimum dwell time by means of a family of quadratic Lyapunov functions. Interestingly, the proposed stability condition does not require the Lyapunov function be uniformly decreasing at every switc...

We show that for any positive integer d, there are families of switched linear systems—in fixed dimension and defined by two matrices only—that are stable under arbitrary switching but do not admit (i) a polynomial Lyapunov function of degree ≤ d, or (ii) a polytopic Lyapunov function with ≤ d facets, or (iii) a piecewise quadratic Lyapunov function with ≤ d pieces. This implies that there cann...