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

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 in [12]. 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 `2-gain computation without introducing additional conservatism. Several examples are presented to show the effectiveness of the approach.