COPRIME FACTORIZATIONS FOR PARAMETER-DEPENDENT SYSTEMS

This paper presents new theory and algorithms for the determination of coprime factorizations for parameter-dependent systems. The obtention of the normalized coprime factors for a LTI plant is revisited. It is shown that the obtention of normalized coprime factors reduces to a special H2 filtering problem. This idea generalizes naturally to polytopic and parameter-dependent systems. Sufficient conditions for the determination of a static observer matrix gain that ensures a certain H2 norm attenuation over the parameter space are given in terms of a finite number of linear matrix inequalities (LMIs). These conditions lead to a unique coprime factorization representation. A numerical example is given to illustrate the theoretical results.