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• W3044473742 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." @default.
• W3044473742 created "2020-07-29" @default.
• W3044473742 creator A5027835055 @default.
• W3044473742 date "2020-07-21" @default.
• W3044473742 modified "2023-09-23" @default.
• W3044473742 title "Converse Barrier Functions via Lyapunov Functions" @default.
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• W3044473742 doi "https://doi.org/10.48550/arxiv.2007.11086" @default.
• W3044473742 hasPublicationYear "2020" @default.
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