Design of an optimal preview controller for a kind of discrete-time system with time-delay

A kind of linear discrete-time system with state time-delay and multirate control setting was studied. By using the methods of lifting technique, difference operator and state vector augmentation, the state equation was changed to another equation with no time-delay. And the multirate preview control problem was reduced to the single-rate one which includes an integrator. The desired preview controller was obtained by the standard linear quadratic (LQ) optimal preview control theory. The applicability of the present results was verified by a numerical example.