Generalized LFT-based representation of parametric uncertain models

In this paper we introduce a general descriptor-type LFT representation of rational parametric matrices. This generalized representation allows to represent arbitrary rationally dependent multivariate functions in LFT-form. As applications, we develop explicit LFT realizations of the transfer-function matrix of a linear descriptor system whose state space matrices depend rationally on a set of uncertain parameters. The resulting descriptor LFT-based uncertainty models generally have smaller orders than those obtained by using the standard LFT-based modelling approach.