Robust Predictor Feedback for Discrete-Time Systems with Input Delays

TL;DR

This paper develops a robust predictor feedback method for discrete-time systems with input delays, enhancing stability and robustness against modeling errors through a Lyapunov redesign approach.

Contribution

It introduces a Lyapunov redesign procedure to improve robustness of predictor feedback in discrete-time systems with input delays, especially under uncertainties.

Findings

Backstepping-based feedback law matches continuous-time predictor feedback.

Sensitivity to modeling errors increases with delay, but is mitigated by the proposed method.

The designed nonlinear feedback guarantees robust global exponential stability.

Abstract

This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping coincides with the predictor-based feedback law used in continuous-time systems with input delays. However, simple examples demonstrate that the sensitivity of the closed-loop system with respect to modeling errors increases as the value of the delay increases. The paper proposes a Lyapunov redesign procedure which can minimize the effect of the uncertainty. Specific results are provided for linear single-input discrete-time systems with multiplicative uncertainty. The feedback law that guarantees robust global exponential stability is a nonlinear, homogeneous of degree 1 feedback law.