Stability radii of linear discrete‐time systems and symplectic pencils

In this paper, we introduce and analyse robustness measures for the stability of discrete‐time system x ( t + 1) = Ax ( t ) under parameter perturbations of the form A → A + BDC where B,C are given matrices. In particular we characterize the stability radius of the uncertain system x ( t + 1) = ( A + BDC ) x ( t ), D an unknown complex perturbation matrix, via an associated symplectic pencil and present an algorithm for the computation of that radius.