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. doi:10.1137/0328071. https://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 | |||||||||
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| 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 | |||||||||
| Issue or Number: | 6 | |||||||||
| Classification Code: | AMS Subject Headings: 93C35, 47A68 | |||||||||
| DOI: | 10.1137/0328071 | |||||||||
| Record Number: | CaltechAUTHORS:20120508-131811131 | |||||||||
| Persistent URL: | https://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: | 09 Nov 2021 19:51 |
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