Paul K. Wintz and Ricardo G. Sanfelice
Nonlinear Analysis: Hybrid Systems, 2026
Abstract
A method is proposed for analyzing asymptotic stability in conical hybrid systems with modes. A conical hybrid system is a hybrid system where the state is mapped linearly at jumps and flows according to a constant or linear flow maps during flows, and where the flow and jump sets are conical. 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. An abstraction-based method is discussed for reducing the size of the CTG, allowing CTG-based analysis to be applied to systems where the CTG would have infinitely many vertices.
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