Lyapunov stability of linear predictor feedback for time-varying input delay

Author

Krstic, Miroslav

Author_Institution

Dept. of Mech. & Aerosp. Eng., Univ. of California, La Jolla, CA, USA

fYear

2009

fDate

15-18 Dec. 2009

Firstpage

1336

Lastpage

1341

Abstract

For LTI systems with a time-varying input delay, an explicit formula for predictor feedback was presented by Nihtila in 1991. In this note we construct a time-varying Lyapunov functional for the closed-loop system and establish exponential stability. The key challenge is the selection of a state for a transport PDE, which has a non-constant propagation speed, and which is the basis of the stability analysis. We illustrate the design and its conditions with several examples. We also develop an observer equivalent of the predictor feedback design, for the case of time-varying sensor delay.

Keywords

Lyapunov methods; asymptotic stability; closed loop systems; delays; feedback; time-varying systems; Lyapunov stability; closed-loop system; exponential stability; linear predictor feedback; predictor feedback design; stability analysis; time varying Lyapunov functional; time-varying input delay; time-varying sensor delay; Backstepping; Control systems; Delay systems; Hydraulic actuators; Kernel; Linear systems; Lyapunov method; Stability analysis; State feedback; Time varying systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on

Conference_Location

Shanghai

ISSN

0191-2216

Print_ISBN

978-1-4244-3871-6

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2009.5400095

Filename

5400095