A Parameter-Dependent Approach to Robust H∞ Control of Norm Bounded Uncertain Systems

Abstract

A new approach to analyze and synthesize linear uncertain systems with time varying norm bounded uncertainty is presented in this paper. First, the uncertainty set is separated into several different sets according to the maximum singular value of uncertainty.Based on the new classification, the original uncertain system is transformed into a Markovian jump system. Second, via a parameter-dependent Lyapunov function, the problems of robust H∞ analysis and synthesis is studied.Based on this, two sufficient conditions for designing parameter-dependent controllers are established. Finally, numerical simulations are used to illustrate the developed method.