Robust compensation of a chattering time-varying input delay with jumps

We investigate the design of a prediction-based controller for a linear system subject to a time-varying input delay, not necessarily First-In/First-Out (FIFO). This means that the input signals can be reordered. The feedback law uses the current delay value in the prediction. It does not exactly compensate for the delay in the closed-loop dynamics but does not require to predict future delay values, contrary to the standard prediction technique. Modeling the input delay as a transport Partial Differential Equation, we prove asymptotic stabilization of the system state, that is, robust delay compensation, providing that the average ℒ2-norm of the delay time-derivative over some time-window is sufficiently small and that the average time between two discontinuities (average dwell time) is sufficiently large.