On the determination of the order and the degree of a zero of a rational matrix

Abstract

A simple formula for the order and the degree of a zero of a multivariable system at a point p <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> of the complex plane is deduced using the Laurent expansion of the transfer function at the point p <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> The formula avoids the need for computing the inverse or generalized inverse of the matrix, and allows easy determination of factorable elementary factors.