On the equivalence between functionally affine LPV state-space representations and LFT models

TL;DR

This paper introduces a transformation method that converts a specific class of LPV systems with affine parameter dependence into LFT models, preserving system behavior and minimality, with the uncertainty block linear in scheduling variables.

Contribution

It provides a novel transformation algorithm for affine LPV systems into LFT models that maintains input-output behavior and minimality.

Findings

Transformation preserves system behavior

Uncertainty block linear in scheduling variables

Minimality of the transformed system

Abstract

We propose a transformation algorithm for a class of Linear Parameter-Varying (LPV) systems with functional affine dependence on parameters, where the system matrices depend affinely on nonlinear functions of the scheduling varable, into Linear Fractional Transformation (LFT) systems. The transformation preserves input-output behavior and minimality, and the uncertainity block of the resulting LFT system is linear in the scheduling variables of the LPV system.