Strong stability exponential bound improvement for mode-constrained switching impulsive systems

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 for nonlinear switched impulsive systems. We consider 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. We provide an example that shows how to ensure the stability robustness of nonlinear systems with a global state weak linearisation.