Affine Characterizations of Minimal and Mode-Dependent Dwell-Times for Uncertain Linear Switched Systems

An alternative approach for minimum and mode-dependent dwell-time characterization for switched systems is derived. While minimum-dwell time results require the subsystems to be asymptotically stable, mode-dependent dwell-time results can consider unstable subsystems and dwell-times within a, possibly unbounded, range of values. The proposed approach is related to Lyapunov looped-functionals, a new type of functionals leading to stability conditions affine in the system matrices, unlike standard results for minimum dwell-time. These conditions are expressed as infinite-dimensional LMIs which can be solved using recent polynomial optimization techniques such as sum-of-squares. The specific structure of the conditions is finally utilized in order to derive dwell-time stability results for uncertain switched systems. Several examples illustrate the efficiency of the approach.