A Characterization of All Solutions to the Four Block General Distance Problem
- 1 March 1991
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control and Optimization
- Vol. 29 (2) , 283-324
- https://doi.org/10.1137/0329016
Abstract
All solutions to the four block general distance problem which arises in H∞ optimal control are characterized. The procedure is to embed the original problem in an all-pass matrix which is constructed. It is then shown that part of this all-pass matrix acts as a generator of all solutions. Special attention is given to the characterization of all optimal solutions by invoking a new descriptor characterization of all-pass transfer functions. As an application, necessary and sufficient conditions are found for the existence of an H∞ optimal controller. Following that, a descriptor representation of all solutions is derivedKeywords
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