Convex lifted conditions for robust stability analysis and stabilization of linear discrete-time switched systems

Abstract

Stability analysis of discrete-time switched systems under minimum dwell-time is studied using a new type of LMI conditions. These conditions are convex in the matrices of the system and shown to be equivalent to the nonconvex conditions proposed by Geromel and Colaneri. The convexification of the conditions is performed by a lifting process which introduces a moderate number of additional decision variables. The convexity of the conditions can be exploited to extend the results to uncertain systems, control design and $\ell_2$-gain computation without introducing additional conservatism. Several examples are presented to show the effectiveness of the approach.