Quadratic Optimal control of linear systems with time-varying input delay

In this paper the optimal control problem for linear time-varying systems with delay in the control input is investigated, in the time-continuous framework. This note aims to propose a different functional approach, whose versatility could result successful in applying it to the case of time-varying delays. The optimal solution at the current time t is proven to be a feedback from the state of the system at time t, provided that a Riccati-like integral differential equation admits solutions.