Sufficient conditions for forward invariance and contractivity in hybrid inclusions using barrier functions
Abstract
This paper studies set invariance and contractivity in hybrid systems modeled by hybrid inclusions using barrier functions. After introducing the notion of a multiple barrier functions, we investigate the tightest possible sufficient conditions to guarantee different forward invariance and contractivity notions of a closed set for hybrid systems with nonuniqueness of solutions and solutions terminating prematurely. More precisely, we consider forward (pre-)invariance of sets, which guarantees solutions to stay in a set, and (pre-)contractivity, which further requires solutions that reach the boundary of the set to evolve (continuously or discretely) towards its interior. Our conditions for forward invariance and contractivity involve infinitesimal conditions in terms of multiple barrier functions. Examples illustrate the results. Keywords: Forward invariance, contractivity, barrier functions, hybrid dynamical systems.
Keywords
Cite
@article{arxiv.1908.03980,
title = {Sufficient conditions for forward invariance and contractivity in hybrid inclusions using barrier functions},
author = {Mohamed Maghenem and Ricardo G. Sanfelice},
journal= {arXiv preprint arXiv:1908.03980},
year = {2022}
}
Comments
Technical report accompanying the paper entitled: Sufficient conditions for forward invariance and contractivity in hybrid inclusions using barrier functions, submitted to Automatica, 2019