Robust predictor feedback for discrete-time systems with input delays

This work studies the design problem of feedback stabilisers 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 modelling errors increases as the value of the delay increases. The paper proposes a Lyapunov redesign procedure that can minimise 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.