On Coprime factors for Parameter-Dependent Systems

Abstract

This paper presents theory and algorithms for the determination of coprime factorizations for parameter-dependent systems. We shall see that the obtention of coprime factors for polytopic and parameter-dependent systems reduces to a generalized H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> filtering problem. The coprime factors are obtained thank to a static observer matrix gain that ensures a certain H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm attenuation over the parameter space. The calculation of such an observer gain is done through a finite number of linear matrix inequalities (LMIs). An example illustrates the theoretical results