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Modeling and Realization of n-Dimensional Linear Discrete Systems

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Abstract

Using a general model for multidimensional linear discrete systems, a new non-minimal real ARMA realization is given for n-dimensional systems in AR forms. A definition of minimality which is compatible with both the underlying theory and its engineering applications, and some necessary conditions for minimality of multidimensional systems are given.

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References

  1. S. Attasi, “Systèmes Lineaires Homogènes À Deux Indices,” Rapport Laboria, no.31, 1973.

  2. R. B. Roesser, “A Discrete State Space Model for Linear Image Processing,” IEEE Transaction on Automatic Control, vol.AC–20, no. 1, February 1975, pp. 1–10.

    Google Scholar 

  3. E. Fornasini and G. Marchesini, “State–Space Realization Theory of Two–Dimensional Filters,” IEEE Transaction on Automatic Control, vol. AC–21, no. 4, August 1976, pp. 716–722.

    Google Scholar 

  4. L. Baratchart, “On Discrete N–dimensional Linear Constant Systems,” Frequency Domain and State Space Methods for Linear Systems, C. I. Byrnes and A. Lindquist (Eds.), 1986, pp. 3–8.

  5. J. Klamka, “Controllability of M–dimensional systems,” Foundations of Control Engineering, vol. 8, no. 2, 1983, pp. 65–74.

    Google Scholar 

  6. T. Kaczorek, Linear Control Systems, vol. 2, John Willey and Sons Inc., 1992.

  7. P. Rocha, Structure and Representation of 2–D Systems, PhD Thesis, Mathematics Institute of the University of Groningen, February 1990.

  8. J. C. Willems, “From Time–series to Linear Systems, Part I: Finite Dimensional Linear Time–invariant Systems,” Automatica, vol. 22, no. 5, 1986, pp. 561–580.

    Google Scholar 

  9. S. Kung, B. C. Levy, M. Morf and T. Kailath, “New Results in 2–D Systems Theory, Part II,” Proceedings of The IEEE, vol. 65, no. 6, 1977, pp. 945–961.

    Google Scholar 

  10. P. Rocha, and J. C. Willems, “Canonical Computational forms for AR 2–D Systems,” Multidimensional Systems and Signal Processing, vol. 1, 1990, pp. 251–278.

    Google Scholar 

  11. E. Fornasini, P. Rocha, and S. Zampieri, “State–Space Realization Theory of 2–D Finite–Dimensional Behaviours,” SIAM Journal of Control and Optimization, vol. 31, no. 6, 1993, pp. 1502–1517.

    Google Scholar 

  12. J. E. Kurek, “The General State–Space Model for a Two–Dimensional Linear Digital System,” IEEE Transaction on Automatic Control, vol. AC–30, no. 6, June 1985, pp. 600–602.

    Google Scholar 

  13. E. Fornasini and G. Marchesini, “Doubly–Indexed Dynamical Systems: State–Space Models and Structural Properties,” Mathematical Systems Theory, vol. 12, 1978, pp. 59–72.

    Google Scholar 

  14. K. Galkowski, “Matrix Description of Multivariable Polynomial,” Linear Algebra and Its Applications, vol. 234, 1996, pp. 209–226.

    Google Scholar 

  15. N. M. Smart and S. Barnett, “The Algebra of Matrices in N–dimensional Systems,” IMA Journal of Mathematical Control and Information, vol. 6, 1989, pp. 121–133.

    Google Scholar 

  16. F. L. Lewis, “A Review of 2–D Implicit Systems,” Automatica, vol. 29, no. 2, 1992, pp. 345–354.

    Google Scholar 

  17. J. D. Aplevich, “Implicit Linear Systems,” Lecture Notes in Control and Information Sciences, Springer–Verlag, 1991.

  18. J.C. Willems, “Paradigms and Puzzles in the Theory of Dynamical Systems,” IEEE Transaction on Automatic Control, vol. 36, no. 3, March 1991, pp. 259–294.

    Google Scholar 

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Miri, S.A., Aplevich, J.D. Modeling and Realization of n-Dimensional Linear Discrete Systems. Multidimensional Systems and Signal Processing 9, 241–253 (1998). https://doi.org/10.1023/A:1008276619008

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