  This paper discusses the robustness of the constant-delay predictor feedback
in the case of an uncertain time-varying input 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 an LMI-based
sufficient condition ensuring the exponential 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.
