New perturbation bounds for the robust stability of linear state space models

Abstract

In this paper, the problem of robust stability of linear time-invariant systems in state space models is considered. Explicit bounds on linear time-invariant perturbations which do not destabilize the system are given for both unstructured and structured perturbations. These bounds are superior to those reported in the recent literature in two senses: i) they are less conservative and ii) they can be applied to a more general class of systems and perturbations. The bounds are easy to compute numerically. Several simple examples are given to demonstrate the new bounds and compare them with results previously reported.