Constant time-horizon prediction-based stabilization for linear systems with input-dependent input delay

This paper investigates prediction-based stabilization for a class of linear systems subject to input-dependent input delay. The delay under consideration is implicitly defined by an integral relation depending on past values of the input. This situation is frequent in the process industry. We propose here to use a prediction on an horizon equal to the equilibrium value of the delay. By relying on a novel transport Partial Differential Equation (PDE) representation of the delay, encapsulating the input-dependency, we prove local exponential stabilization of the closed-loop system.