Lyapunov Stability of Linear Predictor Feedback for Time-Varying Input Delay

Author

Krstic, Miroslav

Author_Institution

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

Volume

55

Issue

2

fYear

2010

Firstpage

554

Lastpage

559

Abstract

For linear time-invariant 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 partial differential equation, 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; closed loop systems; control system synthesis; delay systems; distributed parameter systems; feedback; linear systems; observers; partial differential equations; stability; time-varying systems; Lyapunov stability; closed-loop system; distributed parameter system; exponential stability; linear predictor feedback; linear time-invariant systems; observer equivalent; predictor feedback design; time-varying Lyapunov functional; time-varying input delay; time-varying sensor delay; transport partial differential equation; Actuators; Control systems; Delay effects; Delay systems; Distributed parameter systems; Lyapunov method; Partial differential equations; Stability analysis; State feedback; Time varying systems; Backstepping; delay systems; distributed parameter systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2009.2038196

Filename

5373886