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TECHNICAL BRIEFS

Robust Regional Eigenvalue-Clustering Analysis for Linear Discrete Singular Time-Delay Systems With Structured Parameter Uncertainties

[+] Author and Article Information
Shinn-Horng Chen

Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, 415 Chien-Kung Road, Kaohsiung 807, Taiwan, Republic of China

Jyh-Horng Chou

Department of Mechanical and Automation Engineering, National Kaohsiung First University of Science and Technology, 1 University Road, Yenchao, Kaohsiung 824, Taiwan, Republic of Chinachoujh@ccms.nkfust.edu.tw

Liang-An Zheng

Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, 415 Chen-Kung Road, Kaohsiung 807, Taiwan, Republic of China

J. Dyn. Sys., Meas., Control 129(1), 83-90 (Apr 27, 2006) (8 pages) doi:10.1115/1.2397156 History: Received October 26, 2004; Revised April 27, 2006

In this paper, the regional eigenvalue-clustering robustness problem of linear discrete singular time-delay systems with structured (elemental) parameter uncertainties is investigated. Under the assumptions that the linear nominal discrete singular time-delay system is regular and causal, and has all its finite eigenvalues lying inside certain specified regions, two new sufficient conditions are proposed to preserve the assumed properties when the structured parameter uncertainties are added into the linear nominal discrete singular time-delay system. When all the finite eigenvalues are just required to locate inside the unit circle, the proposed criteria will become the stability robustness criteria. For the case of eigenvalue clustering in a specified circular region, one proposed sufficient condition is mathematically proved to be less conservative than those reported very recently in the literature. Another new sufficient condition is also proposed for guaranteeing that the linear discrete singular time-delay system with both structured (elemental) and unstructured (norm-bounded) parameter uncertainties holds the properties of regularity, causality, and eigenvalue clustering in a specified region. An example is given to demonstrate the applicability of the proposed sufficient conditions.

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Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Finite eigenvalues distribution of the illustrative example, where the solid line denotes the boundary of the specified region, and the dash-dot line denotes the boundary of the stability region

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