OPTIMAL-DESIGN AND OPTIMAL DIGITAL REDESIGN FOR CONTINUOUS-TIME INPUT TIME-DELAY SYSTEMS

This paper addresses two problems: one is the optimal control of an input-delay time-invariant linear system; and the other is a locally optimal-digital redesign of a continuous-time input time-delay system. It is shown that the fundamental closed-loop poles of the time-delay system designed via a predictor control law are identical to those of the non-delay system with the same system matrices. Thus, the well-developed design methods of linear quadratic regulators for the continuous-time non-delay systems can be directly applied to the input time-delay systems. It is also shown that the optimal digital redesign control law developed is able to allocate optimally the eigenvalues of the closed-loop discrete-time time-delay system to a specific region in the complex z-plane and to match closely the states of the digitally controlled closed-loop time-delay system to those of the original continuous-time input time-delay system. The controllers proposed can be easily implemented, using computers with a relatively longer sampling period and relatively slower computation speed.