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A transfer matrix framework approach to the synthesis of H ∞ controllers
Author(s) -
Tsai MiChing,
Tsai ChinShiong
Publication year - 1995
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4590050302
Subject(s) - matrix (chemical analysis) , transfer (computing) , control theory (sociology) , computer science , algebra over a field , mathematics , control (management) , pure mathematics , chemistry , artificial intelligence , parallel computing , chromatography
This paper presents a transfer matrix framework approach to the now well‐known Riccati solution to the nonsingular H ∞ control problem. The approach taken is a frequency‐domain one based on the concepts of coprime factorization and J‐lossless transfer matrices that lead to the development of relatively simple method for obtaining the state‐space solutions. Using two dual pairs of coupled coprime factorizations of certain chain scattering‐matrices which describe the problem, we derive an identity, analogous to the Bezout identity for all stabilizing controllers, to generate all proper real‐rational H ∞ controllers. We also point out the connections between algebraic Riccati solutions and J‐lossless matrices.