Stability analysis of singularly perturbed switched linear systems

International audienceThis chapter proposes a methodology for stability analysis of singularly perturbed switched linear systems. We emphasize that, besides the stability of each subsystem, we need a dwell-time condition to guarantee the overall system stability. The main results of this study provide a characterization of an upper bound on the dwell time ensuring the overall system’s stability. Remarkably, this bound is the sum of two terms. The first one is an upper bound on the dwell time ensuring stability of the reduced-order linear switched system, which is zero if all the reduced modes share a common Lyapunov function. The magnitude of the second term is of order of the parameter defining the ratio between the two timescales of the singularly perturbed system