Introduction to the mathematical theory of switched systems
Yacine Chitour
University Paris XI
France
Abstract: We will introduce the mathematical tools used in the analysis of switched systems (mainly linear systems), in particular regarding their stability. We shall highlight the role of Lyapunov functions, extremal norms, the notion of "worst trajectory", the "dwell-time" and the joint spectral radius. We will conclude by a panorama of the results concerning the stability of systems submitted to persistence of excitation.