Stability criteria for singularly perturbed linear switching systems

We present some results on the uniform exponential stability of singularly perturbed linear systems undergoing switching. In absence of dwell-time constraints, the switching parameter can evolve on the same time scale as the fast variables, or even faster. We investigate the effect of switching laws evolving at a time scale comparable with the fast variables, describing the corresponding asymptotic effect on the slow variable. Based on this analysis, we propose stability criteria for the overall system, uniform for small values of the parameter of singular perturbation.