Paul K. Wintz and Ricardo G. Sanfelice
8th IFAC Conference on Analysis and Design of Hybrid Systems (In Press), 2024


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 the motion of 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, we propose a CTG-based approach to establish asymptotic stability wi thout constructing a Lyapunov function. Examples illustrate the application of CTG-based analysis for proving pre-asymptotic stability.