Convex lifted conditions for robust ℓ2ℓ2-stability analysis and ℓ2ℓ2-stabilization of linear discrete-time switched systems with minimum dwell-time constraint

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 in Geromel and Colaneri (2006b). 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 ℓ2ℓ2-gain computation without introducing additional conservatism. Several examples are presented to show the effectiveness of the approach.