Journal ArticleDOI
Towards a stability theory of general hybrid dynamical systems
A.N. Michel,Bo Hu +1 more
TLDR
A general comparison theory is developed for the class of hybrid dynamical systems considered herein, making use of stability preserving mappings, and it is shown how these results can be applied to establish some of the Principal Lyapunov Stability Theorems.About:
This article is published in Automatica.The article was published on 1999-03-01. It has received 157 citations till now. The article focuses on the topics: Dynamical systems theory & Linear dynamical system.read more
Citations
More filters
Journal ArticleDOI
Perspectives and results on the stability and stabilizability of hybrid systems
TL;DR: In this paper, the authors introduce the concept of hybrid systems and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems.
Journal ArticleDOI
Uniform stability of switched linear systems: extensions of LaSalle's Invariance Principle
TL;DR: This paper provides a collection of results that can be viewed as extensions of LaSalle's Invariance Principle to certain classes of switched linear systems that can deduce asymptotic stability using multiple Lyapunov functions whose Lie derivatives are only negative semidefinite.
Journal ArticleDOI
Dissipativity Theory for Switched Systems
Jun Zhao,David J. Hill +1 more
TL;DR: A frame work of dissipativity theory for switched systems using multiple storage functions and multiple supply rates is set up, and asymptotic stability is guaranteed under certain "negative" output feedback.
Journal ArticleDOI
Solutions to hybrid inclusions via set and graphical convergence with stability theory applications
Rafal Goebel,Andrew R. Teel +1 more
TL;DR: Using the notion of a hybrid time domain and general results on set and graphical convergence, it is established under weak regularity and local boundedness assumptions that the set of solutions is sequentially compact and ''upper semicontinuous'' with respect to initial conditions and system perturbations.
Journal ArticleDOI
Recent developments on the stability of systems with aperiodic sampling: An overview
Laurentiu Hetel,Christophe Fiter,Hassan Omran,Alexandre Seuret,Emilia Fridman,Jean-Pierre Richard,Silviu-Iulian Niculescu +6 more
TL;DR: This article presents basic concepts and recent research directions about the stability of sampled-data systems with aperiodic sampling, and indicates the sources of conservatism, the problems that remain open and the possible directions of improvement.
References
More filters
Journal ArticleDOI
Multiple Lyapunov functions and other analysis tools for switched and hybrid systems
TL;DR: Bendixson's theorem is extended to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of "continuous switched" systems.
Book
Differential and Integral Inequalities
TL;DR: In this article, the author's mono graph "Differential- und integral-un gleichungen," with the subtitle "und ihre Anwendung bei Abschatzungs und Eindeutigkeitsproblemen" was published.