Stability theory for hybrid dynamical systems

Author

Ye, Hui ; Michel, Anthony N. ; Hou, Ling

Author_Institution

Lab. of Wireless Technol., Lucent Technol., Whippany, NJ, USA

Volume

43

Issue

4

fYear

1998

fDate

4/1/1998 12:00:00 AM

Firstpage

461

Lastpage

474

Abstract

We first formulate a model for hybrid dynamical systems which covers a very large class of systems and which is suitable for the qualitative analysis of such systems. Next, we introduce the notion of an invariant set for hybrid dynamical systems and we define several types of (Lyapunov-like) stability concepts for an invariant set. We then establish sufficient conditions for uniform stability, uniform asymptotic stability, exponential stability, and instability of an invariant set of hybrid dynamical systems. Under some mild additional assumptions, we also establish necessary conditions for some of the above stability types (converse theorems). In addition to the above, we also establish sufficient conditions for the uniform boundedness of the motions of hybrid dynamical systems (Lagrange stability). To demonstrate the applicability of the developed theory, we present specific examples of hybrid dynamical systems and we conduct a stability analysis of some of these examples

Keywords

Lyapunov methods; feedback; nonlinear dynamical systems; sampled data systems; stability; Lagrange stability; Lyapunov stability; asymptotic stability; exponential stability; feedback; hybrid dynamical systems; sampled data systems; sufficient conditions; Asymptotic stability; Extraterrestrial measurements; Feedback control; Lagrangian functions; Linear feedback control systems; Logic; Lyapunov method; Stability analysis; Sufficient conditions; Vehicle dynamics;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.664149

Filename

664149