Perturbation bounds for robust stability in linear state space models

Abstract

This paper addresses the aspect of stability robustness of linear systems in the time domain. Upper bounds on the linear perturbation of an asymptotically stable linear system are obtained to maintain stability, both for structured as well as unstructured perturbations using the Lyapunov approach. For structured perturbation the resulting bound is such that it garners the structural information about the nominal (as well as the perturbation) matrix into a single unified expression. In the case of unstructured perturbations, special features of the nominally stable matrix are exploited resulting in simpler expressions for the bound (without the need to solve the Lyapunov equation). Improvement of the proposed measures is illustrated with the help of examples.