An eigenvalue perturbation result for stability bound with respect to biased structured perturbations

Abstract

This paper provides an eigenvalue perturbation result and applies it to the estimation of stability margins for uncertain, linear, discrete-time systems. An upper bound on the norm of a real perturbation maintaining the stability of a given asymptotically stable matrix is computed. It is shown that some other existing unstructured bounds are obtained as particular cases of the estimated stability margin. The main example of application of the estimated bound is relative to the case of structured perturbations given by interval matrices whose non null diagonal elements are not centered around zero. A numerical comparison with other stability bounds proposed in the literature is reported