Convex dwell-time characterizations for uncertain linear impulsive systems

TL;DR

This paper introduces new convex dwell-time conditions for uncertain linear impulsive systems using looped-functionals, enabling analysis of systems with non-monotonic Lyapunov functions and extending to uncertain cases.

Contribution

It proposes a novel approach using looped-functionals for dwell-time analysis, broadening the class of systems that can be analyzed and extending to uncertain systems.

Findings

Conditions are convex and computationally tractable.

Method effectively handles non-monotonic Lyapunov functions.

Examples demonstrate the approach's applicability.

Abstract

New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of functionals suitable for the analysis of hybrid systems. This approach allows to consider Lyapunov functions that evolve non-monotonically along the flow of the system in a new way, broadening then the admissible class of systems which may be analyzed. As a byproduct, the particular structure of the obtained conditions makes the method is easily extendable to uncertain systems by exploiting some convexity properties. Several examples illustrate the approach.