An adaptive Smith-controller for time-delay systems with relative degree n*≤2

This paper addresses the control of time-delay systems whose relative degree does not exceed two. An adaptive Smith controller together with an adaptive law similar to the delay-free case is proposed. By using Lyapunov-Krasovskii functionals for an appropriate model transformation of the original system, semiglobal stability of the closed-loop system and asymptotic convergence of the output error is established. Strict positive realness together with the low relative degree of the plant is exploited to establish the stability properties. Robustness properties of the adaptive controller are briefly discussed.