Conical Transition Graphs for Analysis of Asymptotic Stability in Hybrid Dynamical Systems

Paul K. Wintz and Ricardo G. Sanfelice

8th IFAC Conference on Analysis and Design of Hybrid Systems, 2024

Abstract

A method is proposed for analyzing asymptotic stability in the conical approximation of a hybrid system. Specifically, this paper introduces the conical transition graph (CTG) to simplify the analysis of asymptotic stability in conical approximations by converting solutions to a hybrid system into walks through a discrete graph. By exploiting the fact that pre-asymptotic stability in a conical approximation implies pre-asymptotic stability in the original system, a CTG-based approach can establish asymptotic stability in hybrid systems that have nonlinear flow maps and jump maps without needing to construct a Lyapunov function.

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