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State-space solutions to standard H2 and H(infinity) control problemsSimple state-space formulas are derived for all controllers solving the standard H(infinity) problem of finding, for a given number gamma greater than 0, all controllers such that the H(infinity) norm of the closed-loop transfer function is (strictly) less than gamma. It is known that a controller exists if and only if the unique stabilizing solutions to two algebraic Riccati equations are positive definite and the spectral radius of their product is less than gamma squared. Under these conditions, a parameterization of all controllers solving the problem is given as a linear fractional transformation (LFT) on a contractive stable free parameter. The state dimension of the coefficient matrix for the LFT, constructed using the two Riccati solutions, equals that of the plant and has a separation structure reminiscent of classical LQG (i.e., H2) theory. A standard H2 solution is developed in parallel.
Document ID
19890064762
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Doyle, John C.
(California Institute of Technology Pasadena, United States)
Glover, Keith
(Cambridge, University United Kingdom)
Khargonekar, Pramod P.
(Minnesota, University Minneapolis, United States)
Francis, Bruce A.
(Toronto, University Canada)
Date Acquired
August 14, 2013
Publication Date
August 1, 1989
Publication Information
Publication: IEEE Transactions on Automatic Control
Volume: 34
ISSN: 0018-9286
Subject Category
Cybernetics
Accession Number
89A52133
Distribution Limits
Public
Copyright
Other

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