A closed-form optimal control for linear systems with equal state and input delays

This paper presents the optimal regulator for a linear system with equal delays in state and input and a quadratic criterion. The optimal regulator equations are obtained using the maximum principle. Performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulators available for the linear system without delays and for a rational approximation of the original time delay system. Simulation graphs demonstrating better performance of the obtained optimal regulator are included.