Algebraic propeties of irreducible transfer matrices (Q1883848)

The paper studies relations between irreducibility of transfer function matrices of multivariable systems and properties of their minimal realization. Furthermore it is shown that irreducible transfer function matrices have non-robust algebraic structure, because their elements are connected by strict equalities. Therefore, small errors in calculation of transfer matrix coefficients may lead to an arbitrary change of order of minimal realization, and, as a consequence, to an erroneous conclusion about dynamic properties of the plant under consideration.