The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

The mathematical theory of control became a? eld of study half a century ago in attempts to
clarify and organize some challenging practical problems and the methods used to solve …

Ensuring stability of switched linear systems with a guaranteed dwell time is an important
problem in control systems. Several methods have been proposed in the literature to …

In this note, the global exponential stability of discrete-time switched systems under arbitrary
switching is investigated. First, for discrete-time switched nonlinear systems, the global …

We study the stability of an equilibrium of arbitrarily switched, autonomous, continuous-time
systems through the computation of a common Lyapunov function (CLF). The switching …

This article is concerned with the stability problem for the planar linear switched system,
where the real matrices A 1, A 2∈ ℝ2× 2 are Hurwitz and u (·):[0,∞[→{0, 1} is a measurable …

In this paper we discuss the notion of universality for classes of candidate common
Lyapunov functions for linear switched systems. On the one hand, we prove that a family of …

In this paper we characterize various stability notions of nonlinear switching retarded
systems by the existence of a common Lyapunov--Krasovskii functional with suitable …

Despite the pervasiveness of sum of squares (sos) techniques in Lyapunov analysis of
dynamical systems, the converse question of whether sos Lyapunov functions exist …

We consider switched systems on Banach and Hilbert spaces governed by strongly
continuous one-parameter semigroups of linear evolution operators. We provide necessary …