A LMI condition for the Robustness of Linear Predictor Feedback with Respect to Time-Varying Input Delays

This paper discusses the robustness of the predictor feedback in the case of an unknown time varying delay. Specifically, we study the stability of the closed-loop system when the predictor feedback is designed based on the knowledge of the nominal value of the time-varying delay. By resorting to an adequate Lyapunov-Krasovskii functional, we derive a LMI-based sufficient condition ensuring the asymptotic stability of the closed-loop system for small enough variations of the time-varying delay around its nominal value. These results are extended to the feedback stabilization of a class of diagonal infinite-dimensional boundary control systems in the presence of a time-varying delay in the boundary control input.

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