Stability analysis of singularly perturbed switched and impulsive linear systems

摘要

This paper proposes a new methodology for stability analysis of singularly perturbed linear systems whose dynamics is affected by switches and state jumps. The overall problem is formulated in the framework of hybrid singularly perturbed systems and we use Lyapunov-based techniques to investigate its stability. We emphasize that, beside the stability of slow and fast dynamics, we need a dwell-time condition to guarantee the overall singularly perturbed system is globally asymptotically stable. Furthermore, we characterize this dwell-time as the sum of one term related to the stabilization of systems evolving on one time-scale (slow dynamics) and one term of the order of the parameter defining the ratio between the time-scales. As highlighted in the paper the second term is required to compensate the effect of the jumps introduced in the state of the boundary layer system by the switches and impulses affecting the overall dynamics. Some numerical examples illustrates our results.