Reduction of a Transfer Function via an Observability Matrix
Stephen Mark Barnett · SIAM Journal on Matrix Analysis and Applications · 1994
An algorithm is given for reduction of a scalar transfer function $g( s )$ to its lowest terms. The main step is to reduce the observability matrix for a controllable canonical form state-space realization of $g( s )$ to a block-triangular form by row operations. No polynomial manipulations are required and only a single rank computation is needed. As a byproduct, other properties of the numerator and denominator of $g( s )$ are obtained with little extra effort. The method can be extended to the case when a basis of orthogonal polynomials is used.