Prescribed-time predictor control of LTI systems with input delay

This paper deals with the problem of prescribed-time stabilization of controllable linear systems with input delay. The problem is reformulated under a cascade PDE-ODE setting from which a prescribed-time predictor feedback is designed based on the backstepping approach, and whose transformation makes use of time-varying kernels. The bounded invertibility of the transformation is guaranteed. It is proved that the solution converges to the equilibrium in a prescribed-time. A simulation example is presented to illustrate the results.