Robust eigenvalue-clustering in a specified circular region for linear uncertain discrete singular systems with state delay

In this paper, 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.