Title :
An explicit formula for general H∞ control
Author :
Tsai, Chin-Shinng ; Tsai, Mi-Ching ; Sun, York-Yih
Author_Institution :
Dept. of Electr. Eng., Nat. Cheng Kung Univ., Tainan, Taiwan
Abstract :
This paper extends the result of M.C. Tsai and C.S. Tsai (see IEEE Trans. Automat. Contr., vol.38, p.1416-21, 1993) to a general H∞ control problem which only requires the stabilizing assumption on the generalized plant. By introducing coprime factors of the plant, the necessary and sufficient conditions for the existence of a sub-optimal solution are derived completely in the transfer function domain. The solution is obtained via finding a J-contractive and a J-expansive numerator, respectively, of two associated factorizations; this is equivalent to the existence of positive definite solutions of two corresponding Riccati inequalities in the state-space. The aim of the present paper provides a linkage between J-contractive factorizations and linear matrix inequalities, and an explicit state-space formula for constructing H∞ controllers
Keywords :
H∞ control; Riccati equations; control system synthesis; matrix algebra; state-space methods; transfer functions; H∞ controllers construction; J-contractive factorizations; J-contractive numerator; J-expansive numerator; J-lossless system; Riccati inequalities; associated factorizations; coprime factors; explicit state-space formula; general H∞ control; generalized plant; linear matrix inequalities; positive definite solutions; stabilizing assumption; state-space; sub-optimal solution; transfer function domain; Artificial intelligence; Control systems; Control theory; Linear matrix inequalities; Riccati equations; Scattering; Sufficient conditions; Transfer functions;
Conference_Titel :
Industrial Electronics, Control, and Instrumentation, 1996., Proceedings of the 1996 IEEE IECON 22nd International Conference on
Conference_Location :
Taipei
Print_ISBN :
0-7803-2775-6
DOI :
10.1109/IECON.1996.570583
