Explanation of reduced order controller for a class of H_∞ singular control problem

[1] Doyle J C, Glover K, Khargonekar P P, et al. State-space solutions to standard H₂ and H_∞ control problems[J]. IEEE Trans Auto Contr, 1989, AC-34(8):831~847 [2] Iwasaki T, Skelton R E. All controllers for the general H_∞ control problem: LMI existence conditions and state space formulas [J]. Automatica, 1994, 30(8):1307~1317 [3] Xin X, Guo L, Feng C B. Reduced-order controllers for continuous and discrete-time singular H_∞ control problems based on LMI[J] Automatica, 1996, 32(11):1581~1585 [4] 曾建平.基于LMI的H_∞控制问题降阶控制器的存在性研究 . 北京:北京航空航天大学自动化科学与电气工程学院,2000 Zeng Jianping. Study on the existence of reduced-order controllers for general H_∞ control problem LMI-based .Beijing:School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, 2000(in Chinese) [5] Takao Watanabe,Anton A Stoorvogel. Plant zero structure and further order reduction of a singular H_∞ controller[J] Int J Robust Nonlinear Control, 2002,12:591~619 [6] Zhou Kemin, Doyle J C, Glover K. Robust and optimal control[M] Prentice-Hall Inc,1996.327~372 [7] 程 鹏.线性系统理论[M] 北京:北京航空航天大学出版社,1987.43~52 Cheng Peng. Linear system theory[M] Beijing:Beijing University of Aeronautics and Astronautics Press,1987. 43~52(in Chinese)