Dynamic Regulation of 2D Systems: A State-Space Approach zyxwvutsrqponmlkji Mauro Bisiacco zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFE Department of Mathematics and Znformutics University of Udine Udiw, Italy and Ettore Fornasini and Giovanni Marchesini Department of Electronics and Znfonnatics University of Padova Padova, Ztaly zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGF Submitted by Jan C. Willems A BSTRA CT The possibilities of modifying the dynamical behavior of 2D state-space models by output feedback compensation are investigated, and a complete characterization of the closed-loop polynomial varieties is given. It turns out that -plant hidden modes and rank singularities of the transfer function are the unique constraints we have to cope with in the compensator synthesis. The proof of this result is based on algebraic manipulations of 2D MFDs and on a coprime realization algorithm. 1. INTRODUCTION The first contributions [l-3] that discussed the problem of defining dynamical systems with input, output, and state functions depending on two independent variables appeared nearly 15 years ago. In principle, they were motivated by the necessity of investigating recursive structures for processing two-dimensional data. This processing has essentially been performed for a long time using discrete filters given by ratios of polynomials in two indeterminates or by algorithms assigned via difference equations. Thus the idea of input-output description of systems by transfer functions in two indeterminates, as well as LINEAR ALGEBRA AND ITS APPLlCATlONS 122/12.X/124:195-218 (1989) 0 Elsevier Science Publishing Co., Inc., 1989 195 655 Avenue of the Americas, New York, NY 10010 0024-3795/89/$3X