Journal ArticleDOI
Recent trends in the stability analysis of hybrid dynamical systems
TLDR
In this article, a general model of hybrid dynamical systems, which is defined on an arbitrary metric space, is defined. And a variety of Lyapunov and Lagrange stability results are established and made public in a scattering of publications and workshop records.Abstract:
Dramatic progress in computing capabilities has resulted in the synthesis and implementation of increasingly complex dynamical systems. Since such systems frequently exhibit simultaneously several kinds of dynamic behavior in different parts of the system, they are referred to as hybrid dynamical systems. Such systems frequently defy traditional modeling and analysis techniques since the different system components may evolve along different notions of "time", including real time, discrete time, and discrete events. Most investigations of such systems to date involve ad hoc models and tailor-made analysis results. In some recent work, however, a general model has been proposed which contains most of the different classes of hybrid dynamical systems considered in the literature as special cases. At the core of this general model of hybrid dynamical system, which is defined on an arbitrary metric space, is a notion of generalized time. For this class of general hybrid dynamical systems, a variety of Lyapunov and Lagrange stability results have been established and made public in a scattering of publications and workshop records. Our objective in this paper is to present a unified overview of the more important aspects of this work.read more
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Journal ArticleDOI
Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results
Hai Lin,Panos J. Antsaklis +1 more
TL;DR: This paper focuses on the stability analysis for switched linear systems under arbitrary switching, and highlights necessary and sufficient conditions for asymptotic stability.
Journal ArticleDOI
Hybrid dynamical systems
TL;DR: In this paper, the authors present a tutorial on modeling the dynamics of hybrid systems, on the elements of stability theory for hybrid systems and on the basics of hybrid control, focusing on the robustness of asymptotic stability to data perturbation, external disturbances and measurement error.
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
Stability Criteria for Switched and Hybrid Systems
TL;DR: This paper considers the stability of switched systems in which there are constraints on the switching rules, through both dwell-time requirements and state-dependent switching laws, and discusses the theory of Lyapunov functions and the existence of converse theorems.
Book
Switched Linear Systems: Control and Design
Zhendong Sun,Shuzhi Sam Ge +1 more
TL;DR: In this paper, the authors propose a mathematical framework for stabilizing switching for autonomous systems, including controlability, observability, and normal forms, and feedback stabilization and optimization.
References
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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.
Journal ArticleDOI
Stability theory for hybrid dynamical systems
Hui Ye,A.N. Michel,Ling Hou +2 more
TL;DR: A model for hybrid dynamical systems is formulated which covers a very large class of systems and which is suitable for the qualitative analysis of such systems and several types of (Lyapunov-like) stability concepts for an invariant set are defined.