Transfer function matrix synthesis of two-dimensional systems

Abstract

This paper considers the problem of matching the transfer function matrix of a given two-dimensional system to that of a desired two-dimensional model using output feedback. The approach followed is essentially based on the idea of equating the coefficients of the like <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w^{i}z^{j}</tex> terms in the relationship <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_{c}(w,z)= T_{m}(w,z)</tex> where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_{c}(w,z)</tex> is the closed-loop transfer function matrix and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_{m}(w,z)</tex> is the model transfer function matrix. This approach reduces the problem to that of solving a linear system of equations. Furthermore, necessary and sufficient conditions are established for exact matching. An example is included to illustrate the proposed method.