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This paper discusses the robustness of the constant-delay predictor feedbackin the case of an uncertain time-varying input delay. Specifically, we studythe stability of the closed-loop system when the predictor feedback is designedbased on the knowledge of the nominal value of the time-varying delay. Byresorting to an adequate Lyapunov-Krasovskii functional, we derive an LMI-basedsufficient condition ensuring the exponential stability of the closed-loopsystem for small enough variations of the time-varying delay around its nominalvalue. These results are extended to the feedback stabilization of a class ofdiagonal infinite-dimensional boundary control systems in the presence of atime-varying delay in the boundary control input.

An LMI Condition for the Robustness of Constant-Delay Linear Predictor Feedback with Respect to Uncertain Time-Varying Input Delays