Internal model control for a class of uncertain time-delay systems

Robust stability synthesis of a class of uncertain parameter-varying first-order time-delay systems is presented in this paper. Internal model principle is used to design a robust control using ℋ∞ small-gain theorem. The closed-loop system robustness is investigated against bounded variation of the parameters and sensitivity analysis is performed to determine the stability conditions and provide a systematic framework to derive an explicit delay-dependent stability bound for the tuning parameter. The tuning parameter is further refined through performance analysis incorporating the complementary sensitivity function. Finally, the closed-loop response of a typical delay system is demonstrated for various operating conditions and parameters variations.