Dynamic observation-prediction for LTI systems with a time-varying delay in the input

A predictive-based controller is proposed to control LTI systems in presence of time-varying delay in the input. The control method is based on the computation of an approximated (or asymptotic) prediction thanks to a dynamic system. Then, this prediction is “plugged” into any Lipschitz controller that stabilizes the delay-free system. Explicit conditions that guarantee the closed-loop stability are given thanks to a Lyapunov-Krasovskii analysis. A qualitative analysis of these conditions is performed and the results are illustrated in simulation.