A J-Spectral Factorization Approach to ℋ∞ Control
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.
Additional Information
© 1990 Society for Industrial and Applied Mathematics. Received December 27, 1988. Accepted October 27, 1989.Attached Files
Published - GREsiamjco90.pdf
Files
Name | Size | Download all |
---|---|---|
md5:c6b886ab9cf4357c12f5ebe01e691861
|
2.0 MB | Preview Download |
Additional details
- Eprint ID
- 31352
- Resolver ID
- CaltechAUTHORS:20120508-131811131
- Created
-
2012-05-08Created from EPrint's datestamp field
- Updated
-
2021-11-09Created from EPrint's last_modified field