One approximation in the optimal stabilization problem for the system of periodic delayed differential equations

Abstract

We consider the optimal stabilization problem for a system of differential equations with periodic coefficients and delay. New approximation scheme is proposed to replace the initial infinite-dimensional problem with the finite-dimensional problem. Within the special set of admissible controls the approximating continuous optimal stabilization problem is reduced to the equivalent discrete optimal stabilization problem. Formulas for the optimal control law are obtained.