On the reduction of repetitive processes into singular and non-singular Roesser models

Multidimensional Systems and Signal Processing - In this paper we present new methods for the reduction of a polynomial system matrix describing a discrete linear repetitive process, to equivalent...     

Inverses of Multivariable Polynomial Matrices by Discrete Fourier Transforms

The problem of the fast computation of the Moore–Penrose and Drazin inverse of a multi-variable polynomial matrix is addressed. The algorithms proposed, use evaluation-interpolation techniques and the Fast Fourier transform. They proved to be faster than other known algorithms. The efficiency of the algorithms is illustrated via randomly generated examples.     

A new notion of equivalence for discrete time AR representations

We present a new equivalence transformation termed divisor equivalence, that has the property of preserving both the finite and the infinite elementary divisor structures of a square non-singular polynomial matrix. This equivalence relation extends the known notion of strict equivalence, which dealt only with matrix pencils, to the general polynomial matrix case. It is proved that divisor equivalence characterizes in a closed form relation the equivalence classes of polynomial matrices that give rise to fundamentally equivalent discrete time auto-regressive representations.     

On the reduction of 2-D polynomial systems into first order equivalent models

Multidimensional Systems and Signal Processing - In this paper we propose a novel approach for the reduction of a 2-D rectangular polynomial matrix of arbitrary degree, to first-order matrix...     

A permuted factors approach for the linearization of polynomial matrices

In Antoniou and Vologiannidis (Electron J Linear Algebra 11:78–87, 2004; 15:107–114, 2006), a new family of companion forms associated with a regular polynomial matrix T (s) has been presented, using products of permutations of n elementary matrices, generalizing similar results presented in Fiedler (Linear Algebra Its Appl 371:325–331, 2003) where the scalar case was considered. In this paper, extending this “permuted factors” approach, we present a broader family of companion-like linearizations, using products of up to n(n−1)/2 elementary matrices, where n is the degree of the polynomial matrix. Under given conditions, the proposed linearizations can be shown to consist of block entries where the coefficients of the polynomial matrix appear intact. Additionally, we provide a criterion for those linearizations to be block symmetric. We also illustrate several new block symmetric linearizations of the original polynomial matrix T (s), where in some of them the constraint of nonsingularity of the constant term and the coefficient of maximum degree are not a prerequisite.