# Model reduction of 2-D systems via orthogonal series

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## 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 overdetermined linear algebraic system of equations, which may readily be solved to yield the simplified model. When this model approximates adequately 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 Walsh and Chebyshev series Pade block pulse shifting transformation matrix fraction expansion Chebyshev polynomials## Preview

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## References

- P.N. Paraskevopoulos, “Techniques in model reduction for large scale systems,”
*Control and Dynamic Systems: Advances in Theory and Applications*, Academic Press, NY, (Ed., C.T. Leondes), vol. 23, pp. 165–189, 1986.Google Scholar - R. Genesio and M. Milanese, “A note on the derivation and use of reduced-order models,”
*IEEE Trans. Autom. Control*, vol. AC-21, pp. 118–122, 1976.CrossRefGoogle Scholar - J. Hickien and N.K. Sinha, “Model reduction of linear multivariable systems,”
*IEEE Trans. Autom. Control*, vol. AC-25, pp. 1121–1127, 1980.CrossRefGoogle Scholar - N.R. Sandel, P. Varaiya, M. Athans and M.G. Safonov, “Survey of decentralized control methods for large scale systems,”
*IEEE Trans. Autom. Control*, vol. AC-23, pp. 108–128, 1978.CrossRefGoogle Scholar - M.J. Bosley and F.P. Lees, “A survey of simple transfer function derivations from higher order state variable models,”
*Automatica*, vol. 8, pp. 765–775, 1972.CrossRefGoogle Scholar - P.N. Paraskevopoulos, “Pade type order reduction of two dimensional systems,”
*IEEE Trans. on Circuits and Systems*, vol. CAS-27, pp. 413–416, 1980.CrossRefGoogle Scholar - N.K. Bose and S. Basu, “Two-dimensional matrix Pade approximants: Existence, nonuniqueness, and recursive computation,”
*IEEE Trans. Autom. Control*, vol. AC-25, pp. 509–514, June 1980.CrossRefGoogle Scholar - S.J. Varoufakis and P.N. Paraskevopoulos, “Model reduction of two-dimensional systems by continued fraction expansion,”
*Int'l Journal of Modelling and Simulation*, vol. 3, pp. 95–98, 1983.Google Scholar - S.J. Varoufakis and P.N. Paraskevopoulos, “Optimal model reduction of 2-D systems,”
*Proc. Mediterranean Electrotechnical Conference*, Athens, Greece, p. C2.10, 1983.Google Scholar - P.N. Paraskevopoulos, “On the model reduction of 2-D systems,” Proc. IV Polish-English Seminar on Real Time Process Control, Jablonna, Poland, pp. 270–282, 1983.Google Scholar
- P.N. Paraskevopoulos, “Model reduction techniques for 2-D discrete systems,”
*Digital Techniques in Simulation, Communication and Control*, Elsevier Science Publishers, IMACS, pp. 155–160, 1985.Google Scholar - E.I. Jury and K. Premaratne, “Model reduction of two-dimensional systems,”
*IEEE Trans. on Circuits and Systems*, vol. CAS-33, pp. 558–562, 1986.CrossRefGoogle Scholar - W.S. Lu, E.B. Lee and Q.T. Zhang, “Model reduction for two-dimensional systems,”
*Proc. Int'l Symposium on Circuits and Systems*, vol. 1, pp. 79–82, 1986.Google Scholar - R. Subbayan and M.C. Vaithilingam, “Walsh function approach for simplification of linear systems,”
*Proc. IEEE*, vol. 67, pp. 1676–1677, 1979.Google Scholar - I.R. Horng, J.H. Chou and T.W. Yang, “Model reduction of digital systems using discrete Walsh series,”
*IEEE Trans. Autom. Control*, vol. AC-31, pp. 962–964, 1986.CrossRefGoogle Scholar - R.Y. Hwang and Y.P. Shih, “Model reduction of discrete systems via discrete Chebyshev polynomials,”
*Int'l J. Systems Science*, vol. 15, pp. 301–308, 1987.Google Scholar - P.N. Paraskevopoulos, “Chebychev series approach to system identification, analysis and optimal control,”
*Journal of the Franklin Institute*, vol. 316, pp. 135–157, 1983.CrossRefGoogle Scholar - S. Kak, “Binary sequences and redundancy,”
*IEEE Trans. Systems, Man and Cybernetics*, vol. 4, pp. 399–401, 1974.Google Scholar - J.H. Chou and I.R. Horng, “Simple methods for the shift-transformation matrix, direct-product matrix and summation matrix of discrete Walsh series,”
*Int'l J. Control*, vol. 43, pp. 1339–1342, 1986.Google Scholar - T.T. Lee and Y.F. Tsay, Applications of general discrete orthogonal polynomials to optimal control systems,”
*Int'l J. of Control*, vol. 43, pp. 1375–1386, 1986.Google Scholar - K. Shimizu and T. Hirata, “Optimal design using min max criteria for two-dimensional recursive digital filters,”
*IEEE Trans. Circuits and Systems*, vol. CAS-33, pp. 491–501, 1986.CrossRefGoogle Scholar - K. Garg and H. Singh, “Inversion of 2-D continued fraction,”
*Int'l J. Control*, vol. 34, pp. 191–196, 1981.Google Scholar

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© Kluwer Academic Publishers 1991