Plant zero structure and further order reduction of a singular H∞ controller

A new class of reduced-order controllers is obtained for the H8 problem. The reduced-order controller does not compromise the performance attained by the full-order controller. Algorithms for deriving reduced-order H8 controllers are presented in both continuous and discrete time. The reduction in order is related to unstable transmission zeros of the subsystem from disturbance inputs to measurement outputs. In the case where the subsystem has no infinite zeros, the resulting order of the H8 controller is lower than that of the existing reduced-order H8 controller designs which are based on reduced-order observer design. Furthermore, the mechanism of the controller order reduction is analysed on the basis of the two-Riccati equation approach. The structure of the reduced-order H8 controller is investigated.