An optimal regulator for linear systems with multiple state and input delays

Abstract

This paper presents an optimal regulator for a linear system with multiple state and input delays and a quadratic criterion. The optimal regulator equations are obtained reducing the original problem to the linear-quadratic regulator design for a system without delays. 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 two rational approximations of the original time-delay system. Simulation graphs demonstrating better performance of the obtained optimal regulator with respect to the criterion value are included.The results of applying the regulator (12)-(14) to the system (7) are shown in Figure 2, which presents the graphs of the criterion (8) JðtÞ and the control (12) u n ðtÞ in the interval ½0; T: The M. BASIN AND J. PEREZ 50