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An augmented system approach to static output‐feedback stabilization with ℋ︁ ∞ performance for continuous‐time plants
Author(s) -
Shu Zhan,
Lam James
Publication year - 2008
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.1348
Subject(s) - control theory (sociology) , output feedback , extension (predicate logic) , controller (irrigation) , stability (learning theory) , matrix (chemical analysis) , parametrization (atmospheric modeling) , basis (linear algebra) , computer science , control (management) , feedback control , closed loop , mathematics , control engineering , engineering , materials science , physics , geometry , quantum mechanics , artificial intelligence , machine learning , agronomy , composite material , biology , programming language , radiative transfer
This paper revisits the static output‐feedback stabilization problem of continuous‐time linear systems from a novel perspective. The closed‐loop system is represented in an augmented form, which facilitates the parametrization of the controller matrix. Then, new equivalent characterizations on stability and ℋ ∞ performance of the closed‐loop system are established in terms of matrix inequalities. On the basis of these characterizations, a necessary and sufficient condition with slack matrices for output‐feedback stabilizability is proposed, and an iteration algorithm is given to solve the condition. An extension to output‐feedback ℋ ∞ control is provided as well. The effectiveness and merits of the proposed approach are shown through several examples. Copyright © 2008 John Wiley & Sons, Ltd.