A canonical matrix representation of 2-D linear discrete systems

Abstract EN

In this paper, a matrix form analoguous to the companion matrix which is often encountered in the theory of one dimensional (1-D) linear control systems is suggested for a class of polynomials in two indeterminates and real coefficients, here referred to as two dimensional (2-D) polynomials.

These polynomials arise in the context of the theory of 2-D linear discrete control systems.

Necessary and sufficient conditions are also presented under which a matrix is equivalent to this companion form.

Examples are used to illustrate the ideas developed in this paper.