Stability theory of hybrid dynamical systems with time delay

Author

Liu, Xinzhi ; Shen, Jianhua

Author_Institution

Dept. of Appl. Math., Univ. of Waterloo, Ont., Canada

Volume

51

Issue

4

fYear

2006

fDate

4/1/2006 12:00:00 AM

Firstpage

620

Lastpage

625

Abstract

By defining the bounded time lag space and other related concepts, this note formulates the notion of hybrid dynamical systems with time delay, which provides a unified framework for describing a large class of systems and is suitable for qualitative analysis. It also investigates stability properties of invariant sets by the method of Lyapunov functions and the Razumihin techniques. Criteria on uniform stability and uniform asymptotic stability are established for hybrid dynamical systems with time delay. Those criteria are then applied to conduct stability analysis for impulsive delay differential systems and nonlinear sampled-data feedback control systems with time delay.

Keywords

Lyapunov methods; asymptotic stability; delay-differential systems; delays; feedback; nonlinear control systems; sampled data systems; time-varying systems; Lyapunov functions; hybrid dynamical systems; impulsive delay differential systems; nonlinear sampled-data feedback control systems; qualitative analysis; stability theory; time delay; uniform asymptotic stability; Asymptotic stability; Delay effects; Delay systems; Extraterrestrial measurements; Feedback control; Logic; Lyapunov method; Mathematics; Stability analysis; Stability criteria; Hybrid system; Lyapunov function; Razumikhin technique; time delay; uniform asymptotic stability;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2006.872751

Filename

1618835