A constructive approach to stabilizability and stabilization of a class ofnD systems

This paper presents a constructive approach to the problem of output feedba ck stabilizability and stabilization of a class of linear multidimensional (nD, n>2) systems, whose varieties of the ideals generated by the reduced m inors are infinite with respect to not more than two variables. The main id ea of the proposed approach is to decompose the variety of an nD system in this class into a union of several varieties, each of which is defined by p olynomials in just two variables. The new method can be considered as a com bination of Grobner bases and existing results on two-dimensional (2D) digi tal filter stability tests and on stabilizability and stabilization of 2D s ystems. An example is illustrated.