Robust D-stability analysis for linear discrete-time singular systems with structured parameter uncertainties and delayed perturbations

In this paper, the robust D-stability problem (i.e. robust eigenvalue-clustering in a specified circular region problem) of linear discrete-time singular systems with structured (elemental) parameter uncertainties and delayed perturbations is investigated. Under the assumptions that the nominal discrete-time singular 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 the structured (elemental) parameter uncertainties and delayed perturbations are added into the nominal discrete-time singular system. When all the finite eigenvalues lie inside the unit circle of the z plane, the proposed criterion will become the stability robustness criterion. An example is given to demonstrate the applicability of the proposed sufficient condition.