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Journal of Control Science and Engineering
Volume 2007, Article ID 93904, 12 pages
http://dx.doi.org/10.1155/2007/93904
Research Article

The Best Achievable ℋ2 Tracking Performances for SIMO Feedback Control Systems

Shinji Hara,1 Toni Bakhtiar,1 and Masaaki Kanno2

1Department of Information Physics and Computing, The University of Tokyo, 7-3-1 Hongo, Bunkyo-Ku 113-8656, Tokyo, Japan
2Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi-Shi 332-0012, Saitama, Japan

Received 20 August 2006; Revised 10 January 2007; Accepted 12 April 2007

Academic Editor: Sigurd Skogestad

Copyright © 2007 Shinji Hara et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with the inherent ℋ2 tracking performance limitation of single-input and multiple-output (SIMO) linear time-invariant (LTI) feedback control systems. The performance is measured by the tracking error between a step reference input and the plant output with additional penalty on control input. We employ the plant augmentation strategy, which enables us to derive analytical closed-form expressions of the best achievable performance not only for discrete-time system, but also for continuous-time system by exploiting the delta domain version of the expressions.