Regional Eigenvalue-Clustering Robustness Analysis for Linear Discrete Time-Delay Systems with Both Structured and Unstructured Parameter Uncertainties

Abstract

In this paper, the problem of the regional eigenvalue-clustering robustness analysis for linear discrete time-delay systems with both structured (elemental) and unstructured (norm-bounded) parameter uncertainties is investigated. Under the assumption that all the eigenvalues of a linear nominal discrete time-delay system lie within a specified region, a new sufficient condition is proposed to preserve the assumed property when both the structured (elemental) and the unstructured (norm-bounded) parameter uncertainties are added into the linear nominal discrete time-delay system. No restriction is imposed on the shapes of the specified region. When all the eigenvalues are just required to locate inside the unit circle, the proposed criterion will become the robust stability criterion. For the case that the linear discrete time-delay system only subjects to structured (elemental) parameter uncertainties, by two illustrative examples, the presented sufficient condition is shown to be less conservative than the existing one reported recently in the literature.