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A J-Spectral Factorization Approach to ℋ∞ Control

Green, Michael and Glover, Keith and Limebeer, David and Doyle, John (1990) A J-Spectral Factorization Approach to ℋ∞ Control. SIAM Journal on Control and Optimization, 28 (6). pp. 1350-1371. ISSN 0363-0129. http://resolver.caltech.edu/CaltechAUTHORS:20120508-131811131

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Abstract

Necessary and sufficient conditions for the existence of suboptimal solutions to the standard model matching problem associated with ℋ∞ control, are derived using J-spectral factorization theory. The existence of solutions to the model matching problem is shown to be equivalent to the existence of solutions to two coupled J-spectral factorization problems, with the second factor providing a parametrization of all solutions to the model matching problem. The existence of the J-spectral factors is then shown to be equivalent to the existence of nonnegative definite, stabilizing solutions to two indefinite algebraic Riccati equations, allowing a state-space formula for a linear fractional representation of all controllers to be given. A virtue of the approach is that a very general class of problems may be tackled within a conceptually simple framework, and no additional auxiliary Riccati equations are required.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1137/0328071 DOIUNSPECIFIED
http://epubs.siam.org/sicon/resource/1/sjcodc/v28/i6/p1350_s1PublisherUNSPECIFIED
Additional Information:© 1990 Society for Industrial and Applied Mathematics. Received December 27, 1988. Accepted October 27, 1989.
Subject Keywords:ℋ∞ control, J-spectral factorization, indefinite factorization, four block problems, Riccati equations, Nehari’s Theorem
Classification Code:AMS Subject Headings: 93C35, 47A68
Record Number:CaltechAUTHORS:20120508-131811131
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120508-131811131
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31352
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 May 2012 20:35
Last Modified:26 Dec 2012 15:10

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