Prescribed-time predictor control of LTI systems with distributed input delay

This paper deals with prescribed-time stabilization of controllable linear systems with distributed input delay. We model the input delay as a transport PDE and reformulate the original problem as a cascade PDE-ODE system while accounting for the infinite dimensionality of the actuator. We build on reduction-based and backstepping-forwarding transformations to convert the system into a target system having the prescribed-time stability property. Then, we prove the bounded invertibility of the transformations and hence we show that the prescribed-time stability property is preserved into the original problem. To better illustrate the ideas of this approach, we focus first on the scalar case. Then, we give a sketch of the main lines for the general case. To this end, we choose the ODE dynamics of the target system to be a Linear Time-Varying system so that we can rely on recent developments which include a polynomial-based Vandermonde matrix and the generalized Laguerre polynomials that allow a compact formulation for the stability analysis. A simulation example is presented to illustrate the obtained results.