A Razumikhin approach for the incremental stability of delayed nonlinear systems

Author

Chaillet, Antoine ; Pogromsky, Alexander Yu ; Ruffer, Bjorn S.

Author_Institution

Supelec L2S, Univ. Paris Sud 11, Gif-sur-Yvette, France

fYear

2013

fDate

10-13 Dec. 2013

Firstpage

1596

Lastpage

1601

Abstract

This paper provides sufficient conditions for the incremental stability of time-delayed nonlinear systems. It relies on the Razumikhin-Lyapunov approach, which consists in invoking small-gain arguments by treating the delayed state as a feedback perturbation. The results are valid for multiple delays, as well as bounded time-varying delays. We provide conditions under which the limit solution of a time-delayed nonlinear system in response to a periodic (resp. constant) input is itself periodic and of the same period (resp. constant). As an illustration, a specific focus is given on a class of delayed Lur´e systems.

Keywords

Lyapunov methods; asymptotic stability; delay systems; feedback; nonlinear control systems; periodic control; time-varying systems; Razumikhin approach; Razumikhin-Lyapunov approach; bounded time-varying delays; delayed Lur´e systems; delayed state; feedback perturbation; incremental stability; multiple delays; periodic input; small-gain arguments; sufficient conditions; time-delayed nonlinear systems; Asymptotic stability; Convergence; Delays; Nonlinear systems; Oscillators; Stability analysis; Stress;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on

Conference_Location

Firenze

ISSN

0743-1546

Print_ISBN

978-1-4673-5714-2

Type

conf

DOI

10.1109/CDC.2013.6760110

Filename

6760110