# Plant zero structure and further order reduction of a singular $H_\infty$ controller

Takao Watanabe, Antonie Arij Stoorvogel

14 Citations (Scopus)

## Abstract

A new class of reduced-order controllers is obtained for the $H_\infty$ problem. The reduced-order controller does not compromise the performance attained by the full-order controller. Algorithms for deriving reduced-order $H_\infty$ 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 $H_\infty$ controller is lower than that of the existing reduced-order $H_\infty$ 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 $H_\infty$ controller is investigated.
Original language Undefined 10.1002/rnc.664 591-619 29 International journal of robust and nonlinear control 12 7 https://doi.org/10.1002/rnc.664 Published - 2002

## Keywords

• EWI-16625
• Transmission zeros
• $H_\infty$ control
• IR-68901
• Reduced-order controller design