Strong exponential stability of switched impulsive systems with mode-constrained switching (2311.07751v2)

Abstract: Strong stability, defined by bounds that decay not only over time but also with the number of impulses, has been established as a requirement to ensure robustness properties for impulsive systems with respect to inputs or disturbances. Most existing results, however, only consider weak stability, where the bounds only decay with time. In this paper, we provide a method for calculating the maximum overshoot and the decay rate for strong global uniform exponential stability bounds for nonlinear switched impulsive systems. We consider the scenario of mode-constrained switching where not all transitions between subsystems are allowed, and where subsystems may exhibit unstable dynamics in the flow and/or jump maps. Based on direct and reverse mode-dependent average dwell-time and activation-time constraints, we derive stability bounds that can be improved by considering longer switching sequences for computation. We provide an example that shows how the results can be employed to ensure the stability robustness of nonlinear systems that admit a global state weak linearization.