2019/08/11 by Mohamed Maghenem, Maghenem, Mohamed, Ricardo G. Sanfelice +1
Computer Science · Engineering · #Advanced Control Systems Optimization #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.1908.03980
openalex publication_date 2019/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies set invariance and contractivity in hybrid systems modeled\nby hybrid inclusions using barrier functions. After introducing the notion of a\nmultiple barrier functions, we investigate the tightest possible sufficient\nconditions to guarantee different forward invariance and contractivity notions\nof a closed set for hybrid systems with nonuniqueness of solutions and\nsolutions terminating prematurely. More precisely, we consider forward\n(pre-)invariance of sets, which guarantees solutions to stay in a set, and\n(pre-)contractivity, which further requires solutions that reach the boundary\nof the set to evolve (continuously or discretely) towards its interior. Our\nconditions for forward invariance and contractivity involve infinitesimal\nconditions in terms of multiple barrier functions. Examples illustrate the\nresults. Keywords: Forward invariance, contractivity, barrier functions, hybrid\ndynamical systems.\n