ON RATIONAL BEZOUT EQUATION

HROMČÍK, M.; LIDINSKÝ, J.; ŠEBEK, M.

Abstract

A new algorithm for finding a particular solution of the Bezout equation over the ring of stable proper rational functions is presented in this report. The method is based on the state-space description of involved rational functions and relies on the observability and controllability analysis of input arguments. The method is applicable for the matrix case as well. The developed procedure is accompanied by a simple example and its properties are depicted by means of numerical experiments using the MATLAB computational environment and the Polynomial Toolbox. Although the numerical properties are not superior to other computational approaches to the Bezout identity, as explained in the paper and demonstrated by results of numerical testing, the procedure itself provides a nice insight into the controllability and observability issues and is quite interesting in our opinion. Up to our knowledge, this routine is completely original. Its performance is compared with existing algorithms.

Coresponding author e-mail: m[dot]hromcik[at]c-a-k[dot]cz

Session: Algorithms and Computing for Control