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Zbl 1113.93074
Chen, Shinn-Horng; Chou, Jyh-Horng
Robust eigenvalue-clustering in a specified circular region for linear uncertain discrete singular systems with state delay. (English)
[J] Appl. Math. Comput. 186, No. 2, 1660-1670 (2007). ISSN 0096-3003

Summary: The robust eigenvalue-clustering in a specified circular region problem (i.e., the robust $D$-stability 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 a specified circular region, a new sufficient condition is 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 of the $z$-plane, the proposed criterion will become the stability robustness criterion. The presented criterion is mathematically proved to be less conservative than the existing ones reported very recently in the literature.

MSC 2000:: *93C55 Discrete-time control systems
93D05 Lyapunov and other classical stabilities of control systems
93C05 Linear control systems

Keywords: $D$-stability robustness; singular systems; structured parameter uncertainties; state delay

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Zentralblatt MATH Berlin [Germany]