Robust Stability of Linear Continuous/Discrete-Time Output Feedback Systems with Both Time-Varying Structured and Unstructured Uncertainties

Abstract

This paper investigates the stability robustness of linear continuous/discrete-time systems with output feedback controllers as well as both time-varying structured and unstructured parameter uncertainties by directly considering the mixed quadratically-coupled uncertainties in the problem formulation. Based on the Lyapunov approach and some essential properties of matrix measures, some new sufficient conditions are proposed for ensuring that the linear output feedback systems with both time-varying structured and unstructured parameter uncertainties are asymptotically stable. Three numerical examples for continuous-time and discrete-time systems are given to illustrate the application of the presented sufficient conditions, and for the case of only considering time-varying structured parameter uncertainties, the proposed sufficient conditions are shown to be less conservative than the existing ones reported in the literature.