Grobner bases and applications in control and systems

This paper is a tutorial and review paper on the Grobner bases method and some of its applications in control and systems. Although all the results presented in the paper are available in the literature, we give an elementary treatment here, in the hope that it will further bring awareness of and stimulate interest in Grobner bases among researchers in control and systems. We give a brief tutorial on Euclidean Division Algorithm and Grobner bases, with emphasis on solutions to two important mathematical problems which are closely related to the stabilizability and stabilization of linear Multidimensional systems. Applications of Grobner bases to other areas of control and systems are also briefly mentioned.