Hassibi, Babak and Kailath, Thomas
(1998)
*Upper bounds for mixed H^2/H^∞ control.*
In:
Proceedings of the 37th IEEE Conference on Decision and Control, 1998.
Vol.1.
IEEE
, Piscataway, NJ, pp. 652-657.
ISBN 0-7803-4394-8.
https://resolver.caltech.edu/CaltechAUTHORS:20150217-075137959

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## Abstract

We consider the mixed H^2/H^∞ control problem of choosing a controller to minimize the H^2 norm of a given closed-loop map, subject to the H^∞ norm of another closed-loop map being less than a prescribed value γ. Let d_2 and γ_2 denote the H^2 and H^∞ norms for the pure H^2-optimal solution (without any H^∞ constraint), and let d_c and γ_c < γ denote the H^2 and H^∞ norms for any solution that yields an H^∞ norm strictly less than γ (such as, say, the central solution). Then if d_m denotes the optimal H2 norm that can be achieved in the mixed H^2/H^∞ control problem, we show that (d^2_m - d^2_2)/(d^_c - d^2_2) ⩽ ((γ_2 - γ)/(γ_2 - γ_c))^2 < ((γ^2_2 - γ^2)/(γ^2_2 - γ^2_c))^2 < 1.

Item Type: | Book Section | |||||||||
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Additional Information: | © 1998 IEEE. This work was supported in part by DARPA through the Department of Air Force under contract F49620-95-1-0525-P00001 and by the Joint Service Electronics Program at Stanford under contract DAAH04-94-G-0058-P00003. | |||||||||

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DOI: | 10.1109/CDC.1998.760757 | |||||||||

Record Number: | CaltechAUTHORS:20150217-075137959 | |||||||||

Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20150217-075137959 | |||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||

ID Code: | 54851 | |||||||||

Collection: | CaltechAUTHORS | |||||||||

Deposited By: | Shirley Slattery | |||||||||

Deposited On: | 28 Feb 2015 03:25 | |||||||||

Last Modified: | 10 Nov 2021 20:38 |

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