Prediction-based controller for linear systems with stochastic input delay

We study the stabilization problem of a linear time-invariant system with an unknown stochastic input delay. We propose to robustly compensate for the stochastic delay with a constant time horizon prediction-based controller. We prove the mean-square exponential stabilization of the closed-loop system under a sufficient condition, which requires the range of the delay values to be sufficiently narrow and the constant delay used in the prediction-based controller to be chosen in this range. Numerical simulations illustrate the relevance of this condition and the merits of our control design