Title :
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
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;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2009.2038196
