A Stein matrix equation approach for computing coprime matrix fraction description

Abstract

This paper is concerned with the coprime matrix fraction description of linear systems. Analytical solutions are obtained by solving a Stein matrix equation with nilpotent coefficient matrix. An explicit solution consisting of finite summations to the Stein matrix equation is also provided. The proposed approach can be easily transformed into a numerically reliable algorithm if the Stein matrix equation is solved in a numerically stable way. The parametric eigenstructure assignment problem is reconsidered to illustrate the application and efficiency of the proposed approach.