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Journal of Applied Mathematics
Volume 2013, Article ID 150590, 19 pages
Research Article

Novel Observer-Based Suboptimal Digital Tracker for a Class of Time-Delay Singular Systems

1Integrated Logistical Support Center, Chung-Shan Institute of Science and Technology, Taoyuan 32599, Taiwan
2Department of Electrical Engineering, National Ilan University, Ilan 26047, Taiwan
3Graduate Institute of Automation and Control, National Taiwan University of Science and Technology, Taipei 10607, Taiwan

Received 12 July 2013; Accepted 28 September 2013

Academic Editor: Baocang Ding

Copyright © 2013 Nien-Tsu Hu 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.


This paper presents a novel suboptimal digital tracker for a class of time-delay singular systems. First, some existing techniques are utilized to obtain an equivalent regular time-delay system, which has a direct transmission term from input to output. The equivalent regular time-delay system is important as it enables the optimal control theory to be conveniently combined with the digital redesign approach. The linear quadratic performance index, specified in the continuous-time domain, can be discretized into an equivalent decoupled discrete-time performance index using the newly developed extended delay-free model. Additionally, although the extended delay-free model is large, its advantage is the elimination of all delay terms (which included a new extended state vector), simplifying the proposed approach. As a result, the proposed approach can be applied to a class of time-delay singular systems. An illustrative example demonstrates the effectiveness of the proposed design methodology.