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IMA Journal of Mathematical Control and Information 2003 20(2):153-165; doi:10.1093/imamci/20.2.153
© 2003 by Institute of Mathematics and its Applications
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Robust D-stability analysis for linear discrete singular time-delay systems with structured and unstructured parameter uncertainties

Shinn-Horng Chen1

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

In this paper, the robust D-stability problem (i.e. the robust eigenvalue-clustering in a specified circular region problem) of linear discrete singular time-delay systems with structured (elemental) and unstructured (norm-bounded) parameter uncertainties is investigated. Under the assumptions that the linear nominal discrete singular time-delay system is regular and impulse-free, and has all its finite eigenvalues lying inside a specified circular region, a new sufficient condition is proposed to preserve the assumed properties when structured and unstructured 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 of the z-plane, the proposed criterion will become the stability robustness criterion. For the case that the linear discrete singular time-delay system is only subject to structured parameter uncertainties, by an illustrative example, the presented sufficient condition is shown to be less conservative than the existing one reported recently in the literature.

Keywords: robust D-stability analysis; linear discrete singular time-delay systems; structured and unstructured parameter uncertainties.

Received 2 October 2002. Accepted 2 February 2003.


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