On the practical stability for a class of switched system

Abstract

This paper addresses a problem of robust control for a class of switched systems with timedelays. We deal with controllable nonlinear models that satisfy a quasi-Lipschitz condition and include bounded perturbations. The stabilization issue is carried out by two linear feedback controls: the static and the switching one. We also apply the extended version of the invariant ellipsoid method in combination with the Lyapunov-Krasovskii stability approach. Sufficient conditions of practical stability are derived in terms of Linear Matrix Inequalities (LMIs). The result is illustrated by a numerical example.