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The general distance problem in H_∞ synthesis

Chu, Cheng-Chih and Doyle, John C. (1985) The general distance problem in H_∞ synthesis. In: 1985 24th IEEE Conference on Decision and Control. IEEE , Piscataway, NJ, pp. 1311-1316.

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The general distance problem which arises in the general H_∞ optimal control problem is considered. The existence of an optimal solution is proved and the expression of the optimal norm γ_o is obtained from a somewhat abstract operator point of view. An iterative scheme, called γ-iteration, is introduced which reduces the general distance problem to a standard best approximation problem. Bounds for γ_o are also derived. The γ-iteration is viewed as a problem of finding the zero crossing of a function. This function is shown to be continuous, monotonically decreasing, convex and be bounded by some very simple functions. These properties make it possible to obtain very rapid convergence of the iterative process. The issue of model-reduction in H_∞ - synthesis will also be addressed.

Item Type:Book Section
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Doyle, John C.0000-0002-1828-2486
Additional Information:© 1985 IEEE. This work has been supported by Honeywell Internal Research and Development Funding, the Office of Naval Research under ONR Research Grant N00014-82-C-0157, and the U.S. Air Force of Scientific Research Grant F49620-82-C-0090.
Funding AgencyGrant Number
Honeywell IncorporatedUNSPECIFIED
Office of Naval Research (ONR)N00014-82-C-0157
Air Force Office of Scientific Research (AFOSR)F49620-82-C-0090
Record Number:CaltechAUTHORS:20190308-152211485
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Official Citation:C. Chu and J. C. Doyle, "The general distance problem in H∞ synthesis," 1985 24th IEEE Conference on Decision and Control, Fort Lauderdale, FL, USA, 1985, pp. 1311-1316. doi: 10.1109/CDC.1985.268720
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:93682
Deposited By: George Porter
Deposited On:09 Mar 2019 00:23
Last Modified:16 Nov 2021 16:59

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