On the division of polynomial matrices

The main purpose of this paper is to determine two new algorithmsfor the division of the polynomial matrix B(s) R[s]^pxq by A(s) R[s]^pxp (a) based on the Laurent matrix expansion at s = =of the inverse of A(s), i.e. A(s)^–1, and (b) in a waysimilar to the one presented by Gantmacher (1959).     

On a certain McMillan-degree condition appearing in control

The paper presents a number of interpretations of the McMillan-degreeconditions appearing in the transformation of full equivalencedefined by Hayton et al. in 1988. The most satisfactory explanationseems to be that of guaranteeing the existence of a linear mapbetween the solution sets of the ordinary differential equationswhich underly the matrices involved in the transformation.     

Generalized state-space system matrix equivalents of a Rosenbrock system matrix

Bosgra & Van Der Weiden (1981) have given a procedure wherebya Rosenbrock system matrix may be reduced to an equivalent generalizedstate-space system matrix. The sense in which this is equivalentto the original system matrix is that the reduced system matrixexhibits identical system properties both at finite and infinitefrequencies. Hayton et al. (1990) introduced the transformationsof normal full system equivalence and full system equivalence.In the present work, we show that the Bosgra & Van Der Weidenreduction procedure is a full system-equivalence transformation,and a characterization of this equivalence in a matrix-transformationsense is also provided.     

Matrix fractions and full system equivalence

Following the definition by Hayton et al. (1990) of full systemequivalence for linear multivariables systems, the concept offull unimodular equivalence is defined for matrix fraction descriotions(MFDs).Full unimodular equivalence is an extension of unimodular equivalence,which has been proposed by Kailath (1980) and Smith (1981) forsystems described by polynomial matrix models in either leftor right MFD form. Full unimodular equivalence has the propertyof leaving invariant both the finite and infinite structureof the system. It is shown that full unimodular equivalencefor MFDs and full system equivalence coincide.