Stability Robustness of Control Systems Subject to Perturbations in Matrix Form

In this paper two approaches are presented to characterize the allowable perturbations in the unity feedback system matrices such that the system will not be destabilized. The perturbation bound derived here has been related to the eigenstructure of the control systems. It is shown that the perturbation has a lower bound in terms of the condition number of a transformation matrix and the real part of the dominant pole. As an application of the robustness theory, we consider the robust stability analysis of a combined observer-controller problem.