Robust stability and controller synthesis of discrete linear switched systems with dwell time

Abstract

Sufficient conditions are derived for the robust stability of discrete-time, switched, linear systems with dwell time in the presence of polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, is assigned to each of the subsystems. This function is allowed to be time-varying and piecewise linear during the dwell time and it becomes time invariant afterwards. Asymptotic stability conditions are obtained in terms of linear matrix inequalities for the nominal set of subsystems. These conditions are then extended to the case where the subsystems encounter polytopic type parameter uncertainties. The developed method is applied to l ₂-gain analysis where a bounded real lemma is derived, and to H _∞ control and estimation, both for the nominal and the uncertain cases.

Keywords:

• linear switched systems
• dwell time
• discrete-time
• polytopic uncertainties

Acknowledgement

This work was supported by the C&M Maus Chair at Tel Aviv University.