Stability analysis of hybrid dynamical systems using convex Lyapunov functions

Abstract

This study introduces an inequality for analyzing the stability of hybrid dynamical systems using convex Lyapunov functions. Thei nequality establishes that a hybrid dynamical system is stable if there exists a convex and positive-definite Lyapunov function whose time derivative along continuous flows and discrete jumps satisfies specific negativity conditions. This result extends existing methods and provides a practical framework for constructing Lyapunov functions in the stability analysis of hybrid systems. To demonstrate the efficacy of the proposed approach, the study includes illustrative examples supported by numerical simulations.