Robust compensation of a chattering time-varying input delay

We investigate the design of a prediction-based controller for a linear system subject to a time-varying input delay, not necessarily causal. This means that the information feeding the system can be older than ones previously received. We propose to use the current delay value in the prediction employed in the control law. Modeling the input delay as a transport Partial Differential Equation, we prove asymptotic tracking of the system state, providing that the average ℒ
₂
-norm of the delay time-derivative is sufficiently small. This result is obtained by generalizing Halanay inequality to time-varying differential inequalities.