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

摘要

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