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arXiv · 2007.11086

Converse Barrier Functions via Lyapunov Functions

Jun Liu
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Abstract

We prove a robust converse barrier function theorem via the converse Lyapunov theory. While the use of a Lyapunov function as a barrier function is straightforward, the existence of a converse Lyapunov function as a barrier function for a given safety set is not. We establish this link by a robustness argument. We show that the closure of the forward reachable set of a robustly safe set must be robustly asymptotically stable under mild technical assumptions. As a result, all robustly safe dynamical systems must admit a robust barrier function in the form of a Lyapunov function for set stability. We present the results in both continuous-time and discrete-time settings and remark on connections with various barrier function conditions.

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Jun Liu. 2020-07-21. Converse Barrier Functions via Lyapunov Functions. https://doi.org/10.1109/tac.2021.3085419

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