Design of Parametric Controller for Two-Dimensional Polynomial Systems Described by the Fornasini-Marchesini Second Model

Abstract

In this paper, a general parametric controller design method is presented for twodimensional (2D) linear discrete systems described by the Fornasini-Marchesini second model. This method is based on the discriminant systems of polynomial and Hurwitz theorem. By the fractional linear transformation, the problem of stability analysis for 2D systems can be turned to a new problem whether the polynomials are Hurwitz stable. Thus, the process of stability analysis is changed into a problem whether some polynomials are positive definite, which can be easily checked by the discriminant system of the polynomial. It simplifies some existing methods of analyzing stability for 2D systems. Then, we apply the process proposed stability analysis method to consider the stabilization problem. A parametric controller is derived. The form of the parametric controller designed by the proposed method is simple, the parameters of the controller law can be fully solved. Finally, we give two numerical examples and a practical example of a chemical reactor thermal process to show the validity of the proposed methods.INDEX TERMS Parametric controller, 2D system, the Fornasini-Marchesini second model, the discriminant system of polynomial.