Journal of Control Science and Engineering 
Volume 2007 (2007), Article ID 93904, 12 pages
doi: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

Recommended by Sigurd Skogestad

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.