Tool for LPV and LFT Modelling

摘要

This report treats the problem of transforming a parameter varying system to a so211u001ecalled Linear Fractional Transformation (LFT). An automatic method for this 211u001etransformation is suggested and the method is also implemented using the computer 211u001esoftware MATLAB. The report begins with a description and definition of the LFT 211u001eframework. A method is presented for transforming multi-variable rational 211u001efunctions to LFT's and different methods for reducing the order of an LFT are 211u001egiven. Systems theory and methods for transforming nonlinear parameter varying 211u001esystems and linear parameter varying (LPV) systems to LFT's are given. The parts 211u001eof the parameter varying systems that have a nonrational dependence of the 211u001eparameters must be approximated by rational functions before the system can be 211u001etransformed to LFT's. A method for this rational approximation, using the least-211u001esquares method is also given. In order to verify that the developed program works 211u001eit is applied to different systems. These verifications suggest that the program 211u001eworks well for most LPV systems and for some nonlinear parameter varying systems.