Design of optimal output regulators for multirate linear discrete-time descriptor causal system with time delay

This paper introduces the design problem of optimal output regulators for multirate linear discrete-time descriptor causal systems. At first, by making use of the discrete lifting technique the original system is transformed into no state time-delay system in form. Then thought the equivalent transformation, taking advantage of the causal characteristics of the system, it is changed into a normal system. Continuing to apply discrete lifting into the system, a simple single-rate system in form is exported. The performance index function of the original system is modified to that of the single-rate system, and then an optimal output regulator is obtained by using the optimal regulator theory. Through transformation an optimal output regulator for the original system is finally derived. At meantime, the stabilizability and detectability of the exported single-rate system were discussed, and their rigorous mathematical proofs were given. Numerical simulations proved the effectiveness of the preview controller designed in this paper.