REDUCTION OF A TRANSFER-FUNCTION VIA AN OBSERVABILITY MATRIX

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.