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Complete solution of the 4‐block H ∞ control problem with infinite and finite j ω ‐axis zeros
Author(s) -
Xin Xin,
Anderson Brian D. O.,
Mita Tsutomu
Publication year - 2000
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/(sici)1099-1239(200002)10:2<59::aid-rnc461>3.0.co;2-f
Subject(s) - mathematics , transfer function , pole–zero plot , realization (probability) , norm (philosophy) , control theory (sociology) , transfer matrix , matrix (chemical analysis) , riccati equation , complex plane , invariant (physics) , mathematical analysis , control (management) , differential equation , computer science , statistics , materials science , artificial intelligence , political science , law , electrical engineering , composite material , computer vision , mathematical physics , engineering
This paper discusses the 4‐block H ∞ control problem with infinite and finite j ω ‐axis invariant zeros in the state‐space realizations of the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output, where these realizations are induced from a stabilizable and detectable realization of the generalized plant. This paper extends the DGKF approach to the H ∞ control problem but permitting infinite and finite j ω ‐axis invariant zeros by using the eigenstructures related to these zeros. Necessary and sufficient conditions are presented for checking solvability through checking the stabilizing solutions of two reduced‐order Riccati equations and examining matrix norm conditions related to the j ω ‐axis zeros. The parameterization of all suitable controllers is given in terms of a linear fractional transformation involving a certain fixed transfer function matrix and together with a stable transfer function matrix with gain less than 1 which is free apart from satisfying certain interpolation conditions. Copyright © 2000 John Wiley & Sons, Ltd.