Збережено в:
| Автор: | |
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| Формат: | Preprint |
| Опубліковано: |
2020
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| Предмети: | |
| Онлайн доступ: | https://arxiv.org/abs/2007.11086 |
| Теги: |
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Зміст:
- 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.