Exponential stabilization of systems with time-delay by optimal memoryless feedback

A method to construct a memoryless feedback law for system with time-delay in states is proposed. A feedback gain is calculated with a solution of a matrix Riccati equation. It is shown that the memoryless feedback law asymptotically stabilizes the closed loop system and it is an optimal control for some quadratic cost functional. Then, an auxiliary system is introduced and a feedback gain is calculated in the same way. Using this gain, a feedback law for the original plant is re-constructed. It is shown that it gives the resulting closed loop system a pre-assigned exponential stability, and moreover, it is an optimal control for another cost functional. A sufficient condition for the construction of the feedback is presented. A design example is shown, and a numerical simulation is performed.