Distance Measures, Robust Stability Conditions and Robust Performance Guarantees for Uncertain Feedback Systems

Abstract

Given a nominal plant, a perturbed plant, an uncertainty structure and performance weights, we use robust model validation ideas to define and compute a measure of the distance between the nominal and perturbed plants. We also define a stability margin for a feedback system that is related to robust stability and nominal performance, and derive conditions for the stability and bounds for the performance degradation of the perturbed feedback system in terms of the distance measure. These robust stability and robust performance results give the distance measure a feedback interpretation. The simplicity and power of our procedure for computing the distance between two systems is illustrated using a normalized coprime factor uncertainty model to derive results that have already been published in the literature using different techniques. All systems considered in this paper are linear timeinvariant.

Keywords: Robust stability, robust performance, distance measures, model validation, feedback systems, gap metric, ν-gap matric, $\mathcal{H}_\infty$ control, stability margin