LPV Series-Expansion Representations

Abstract

In this chapter, series-expansion representations of LPV systems for a given IO partition are developed using the framework of the behavioral approach. In fact, expansion of DT asymptotically stable LPV systems is considered in terms of OBFs and the connection between this type of expansion and the gain-scheduling principle is explored. It is shown that this series-expansion representation is unique and always exists for the considered system class and in some cases only a finite number of the expansion coefficients are nonzero. This implies that finite truncation of a OBFs-based series-expansion can be used as a model structure for the identification of asymptotically stable DT-LPV systems similar to the LTI case.