Multidimensional Systems and Signal Processing, 2, 69-83 (1991) © 1991 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. Model Reduction of 2-D Systems via Orthogonal Series RN. PARASKEVOPOULOS, P.E. PANAGOPOULOS AND G.K. VAITSIS National Technical University of Athens, Electrical Engineering Department, Division of Computer Science, 15773, Zographou, Athens, Greece. S.J. VAROUFAKIS N. R.C.P S. "Democritos," Institute of Informatics and Telecommunications, 15310Aghia Paraskevi, Athens, Greece G.E. ANTONIOU New Jersey Institute of Technology, Department of Electrical and Computer Engineering, University Heights', Newark, NJ, 07102 Received February 15, 1990, Revised October 4, 1990 Abstract. In this article, the problem of model reduction of 2-D systems is studied via orthogonal series. The algorithm proposed reduces the problem to an overdeterminedlinear algebraic system of equations, which may readily be solved to yield the simplified model. When this model approximatesadequately the original system, it has many important advantages,e.g., it simplifies the analysis and simulation of the original system, it reduces the computational effort in design procedures, it reduces the hardware complexity of the system, etc. Several examples are included which illustrate the efficiency of the proposed method and gives some comparison with other model reduction techniques. Keywords: orthogonal series, model reduction, Walshand Chebyshevseries, Pade, block pulse, shifting transfor- mation matrix, fraction expansion, Chebyshev polynomials. 1, Introduction The model reduction problem aims in simplifying the mathematical description of a system at the cost of having a less accurate model. The major motivations for deriving a reduced order model are the following: a. to simplify analysis of the original system, b. to simplify simulation of the original system, c. to reduce the computational effort in the design of controllers (optimal, adaptive, etc.), and d. to reduce hardware complexity and cost. For the case of 1-D systems many model reduction techniques have been proposed and a large number of related publications have appeared. For an extensive literature on the subject see [Paraskevopoulos 1986; Genesio and Milanese 1976; Hickien and Sinha 1980; Sandel, Varaiya, Athans and Safonov 1978; Bosley and Lees 1972]. For the case of 2-D systems limited results have been reported. In [Paraskevopoulos 1986; Bose and Basu 1980] a Pade type reduced model is derived. In [Varoufakis 1983] the sim- plified model is derived via continued fraction expansion. In [Varoufakis and Paraske- w~poulos 1983] an optimal model reduction technique is proposed. A review of the results