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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