Advertisement

Multidimensional Systems, Signals, Circuits, and Repetitive Processes: Theory, Applications, and Future Trends

  • K. Galkowski
  • A. Kummert

Abstract

In this overview the basics and recent results in multidimensional systems and repetitive processes theory and applications together with future trends are concisely revisited.

Keywords

multidimensional systems repetitive processes 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

9 References

  1. [1]
    Aggarwal J. K., “Principles of multidimensional wave digital filtering”, Digital Signal Processing, Ed. Fettweis A., 262–282, Point Lobo Press, Hollywood, 1979.Google Scholar
  2. [2]
    Amann N., Owens D.H., Rogers E., “Predictive optimal iterative learning control”, Int. J. Control, Vol. 69, No. 2, 203–226, 1998.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Ansell H.G., “On certain two-variable generalizations of circuits theory, with applications to network of transmission lines and lumped reactances”, IEEE Trans. on Circuits and Systems, Vol. CAS-11, 214–223, 1964.Google Scholar
  4. [4]
    Basu S., Fettweis A., “On the factorization of scattering transfer matrices of multidimensional lossless two-ports”, IEEE Trans. on Circuits and Sytems, Vol. CAS-32, 925–934, 1985.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Basu S., Fettweis A., “New results on stable multidimensional polynomials-Part II: Discrete case”, IEEE Trans. on Circuits ans Systems, Vol. 34, No. 11, 1264–1274, 1987.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Bose N.K. (Ed.), Buchberger B. (Ed.), Guiver J.P. (Ed.), “Multidimensional Systems Theory and Applications”, Kluwer Academic Pub., 2004.Google Scholar
  7. [7]
    Boyd S., Ghaoui L. E., Feron E., and Balakrishnan V., “Linear Matrix Inequalities In System And Control Theory”, vol. 15 of SIAM studies in applied mathematics. SIAM, Philadelphia, 1994.Google Scholar
  8. [8]
    Buchberger B., “Ein algorithmishes kriterium fur die losbarkeit eines algebraishen gleichungsystems”, Aeq. Math., Vol. 4, 374–383, 1970.zbMATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    Fettweis A., “Multidimensional wave digital filters”, European Conf. Circuit Theory and Design, Vol. II, 409–416, 1976.Google Scholar
  10. [10]
    Fettweis A., “Multidimensional circuits and systems”, in Proc. IEEE Int. Symp. on Circuits and Systems, Vol. 3, 951–957, 1984.MathSciNetGoogle Scholar
  11. [11]
    Fettweis A., “Some properties of scattering Hurwitz polynomials”, Archiv für Elektronik und Übertragungstechnik, Vol. 38, 171–176, 1984.Google Scholar
  12. [12]
    Fettweis A., “Wave digital filters: Theory and practice”, (invited paper) Proc. of the IEEE, Vol. 74, No. 2, 270–327, 1986.CrossRefGoogle Scholar
  13. [13]
    Fettweis A., “Discrete passive modeling of physical systems described by PDEs”, European Signal Proceeding Conference, Vol. 1, 55–62, 1992.Google Scholar
  14. [14]
    Fettweis A., “Simulation of hydromechanical partial differential equations by discrete passive dy-namical systems”, In Kimura H. et al Eds. Recent Advances in Mathematical Theory of Systems, Control and Signal Processing II, MITA Press, 489–494, 1992.Google Scholar
  15. [15]
    Fettweis A., Basu S., “New results on multidimensional Hurwitz polynomials”, ISCAS, Vol. 3, 1359–1362, 1985.Google Scholar
  16. [16]
    Fettweis A., Basu S., “New results on stable multidimensional polynomials-Part I”: Continuous case”, IEEE Trans. on Circuits ans Systems, Vol. 34, No. 10, 1221–1232, 1987.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    Fettweis A., Linnenberg G., “An extension of the maximum-modulus principle for application to multidimensional networks”, Archiv für Elektronik und Übertragungstechnik, Vol. 38, 131–135, 1984.Google Scholar
  18. [18]
    Fettweis A., Nitsche G., “Numerical integration of partial differential equations by means of multidimensional wave digital filters”, IEEE International Symposium on Circuits and Systems, Vol. 2, 954–957, 1990.CrossRefGoogle Scholar
  19. [19]
    Fettweis A., Nitsche G., “Numerical integration of partial differential equations using principles of multidimensional wave digital filters”, Journal of VLSI Signal Processing, vol. 3, 7–24, 1991.CrossRefzbMATHGoogle Scholar
  20. [20]
    Fettweis A., Seraji G. A., “New results in numerically integrating PDEs by the wave digital approach”, IEEE International Symposium on Circuits and Systems, Vol. 5, 17–20, 1999.Google Scholar
  21. [21]
    Fornasini E., Marchesini G. “Doubly-indexed dynamical systems”, Math. Syst. Theory, Vol. 12, 59–72, 1978.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    Fornasini E., “A 2-D systems approach to river pollution modelling, Multi-dimensional Systems and Signal Processing, Vol. 2, 233–265, 1991.zbMATHMathSciNetCrossRefGoogle Scholar
  23. [23]
    Fornasini E., Zampieri S., “A note on the state space realization of 2D FIR transfer functions”, Systems & Control Letters, Vol. 16, 117–122, 1991.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    Fries M., “Numerical integration of Euler flow by means of multidimensional wave digital principles”, Dissertation, Ruhr-Universität Bochum, 1995.Google Scholar
  25. [25]
    Gałkowski K., Vinnikov V., (Ed.), “International Journal of Control, spec. issue”, 2004, Vol. 77, no 9.Google Scholar
  26. [26]
    Gałkowski K., Longman R. W., Rogers E., (Ed.), “International Journal of Applied Mathematics and Computer Science: Special Issue: Multidimensional Systems nD and Iterative Learning Control”, 2003, Vol. 13, no 1.Google Scholar
  27. [27]
    Galkowski K., “State-space Realizations of Linear 2-D Systems with Extensions to the General nD (n>2) Case”, vol. 263 of Lecture Notes in Control and Information Sciences. Springer, London, 2002.Google Scholar
  28. [28]
    Galkowski K., Wood J., Eds., “Multidimensional Signals, Circuits and Systems”, Taylor & Francis, 2001.Google Scholar
  29. [29]
    Galkowski K., Rogers E., Xu S., Lam J. and Owens D. H., “LMIs-A fundamental tool in analysis and controller design for discrete linear repetitive processes”, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Application, 49(6), pp. 768–778, 2002.MathSciNetCrossRefGoogle Scholar
  30. [30]
    Goodman D,. “Some stability properties of two-dimensional linear shift-invariant filters”, IEEE Trans. on Circuits and Systems, Vol. CAS 24, 201–208, 1977.CrossRefGoogle Scholar
  31. [31]
    Johnson D.S., Rogers E., Pugh A.C., Hayton G.E., Owens D.H., “A polynomial Matrix theory for a certain class of 2-D linear systems”, Linear Algebra and Its Applications, no.241–243, pp 669–703, 1996.MathSciNetCrossRefGoogle Scholar
  32. [32]
    Kaczorek, T., “Linear Control Systems”, Research Studies Press LTD, (distributed by John Wiley & Sons Inc), 1993.Google Scholar
  33. [33]
    Kaczorek T., “2-D continuous-discrete linear systems”, in Proc. Tenth Int. Conf. on System Eng. ICSE'94, Vol. 1, 550–557, 1994.Google Scholar
  34. [34]
    Kailath T., “Linear Systems”, Prentice-Hall, Englewood Cliffs, N.Y., 1980.zbMATHGoogle Scholar
  35. [35]
    Kummert A., “Synthesis of two-dimensional lossless m-ports with prescribed scattering matrix”, Circuits, Systems, and Signal Processing, Vol. 8, No. 1, 97–119, 1989.zbMATHMathSciNetCrossRefGoogle Scholar
  36. [36]
    Kummert A., “On the number of frequency-dependent building elements of multidimensional lossless networks”, Archiv für Elektronik und Übertragungstechnik, Vol. 43, No. 4, 237–240, 1989.Google Scholar
  37. [37]
    Kummert A., “Synthesis of 3-D lossless first-order one-ports with lumped elements”, IEEE Trans. on Circuits and Systems, Vol. CAS-36, No. 11, 1445–1449, 1989.MathSciNetCrossRefGoogle Scholar
  38. [38]
    Kummert A., “Synthesis of two-dimensional passive one-ports with lumped elements, Signal Processing, Scattering and Operator Theory, and Numerical Methods”, Eds. Kaashoek M. A., van Schuppen J. H., Ran A. C. M, International Symposium on Mathematical Theory of Networks and Systems, 1989, Vol. III, 99–106. Birkhäuser, Boston, 1990.Google Scholar
  39. [39]
    Kummert A., “The synthesis of two-dimensional passive n-ports containing lumped elements”, Multidimensional Systems and Signal Processing, Vol. 1, No. 4, 351–362, 1990.zbMATHCrossRefGoogle Scholar
  40. [40]
    Kummert A., “On the synthesis of multidimensional reactance multiports”, IEEE Trans. on Circuits and Systems, Vol. CAS-38, No. 6, 637–642, 1991.CrossRefGoogle Scholar
  41. [41]
    Kummert A., “2-D stable polynomials with parameter-dependent coefficients: Generalisations and results”, IEEE Transactions on Circuits and Systems, Vol. 49, No. 6, pp. 725–731, 2002.MathSciNetCrossRefGoogle Scholar
  42. [42]
    Kurek J.E., “The general state-space model for a two-dimensional digital systems”, IEEE Trans. on Automatic Control, Vol. AC-30, 345–354, 1985.MathSciNetGoogle Scholar
  43. [43]
    Ozaki H., Kasami T., “Positive real functions of several variables and their applications to variable networks”, IRE Trans. on Circuit Theory, Vol. 7, 251–260, 1960.Google Scholar
  44. [44]
    Roberts P.D., “Numerical investigations of a stability theorem arising from the 2-dimensional analysis of an iterative optimal control algorithm”, Multidimensional Systems and Signal Processing, Vol. 11, No. 1/2, 109–124, 2000.zbMATHMathSciNetCrossRefGoogle Scholar
  45. [45]
    Rocha P., “Structure and Representations for 2-D Systems”, PhD Thesis, University of Groningen, The Netherlands, 1990.Google Scholar
  46. [46]
    Roesser R., “A discrete state space model for linear image processing”, IEEE Trans. Automatic Control, vol. 20, pp. 1–10, 1975.zbMATHMathSciNetCrossRefGoogle Scholar
  47. [47]
    Rogers E., Owens D.H., “Stability analysis for linear repetitive processes”, Lecture Notes in Control and Information Sciences, 175, Ed. Thoma M., Wyner W., Springer Verlag, Berlin, 1992.Google Scholar
  48. [48]
    Smyth K., “Computer aided analysis for linear repetitive processes”, PhD Thesis, University of Strathclyde, Glasgow, UK, 1992.Google Scholar
  49. [49]
    Uruski M., Piekarski M., “Synthesis of a network containing a cascade of commensurate transmissions lines and lumped elements”, Proc. IEEE, Vol. 119, No. 2, 153–159, 1972.Google Scholar
  50. [50]
    Vollmer M., An approach to automatic generation of wave digital stzructures from PDEs, IEEE International Symposium on Circuits and Systems, 2004.Google Scholar
  51. [51]
    Youla D.C., Gnavi G. Notes on n dimensional systems, IEEE Trans on Circuits and Systems, Vol. CAS-26, No. 2, 105–111, 1979.MathSciNetCrossRefGoogle Scholar
  52. [52]
    Youla D.C., Pickel P.F., “The Quillen-Suslin theorem and the structure of n-dimensional elementary polynomial matrices”, IEEE Trans. on Circuits and Systems Vol. CAS-31(6):513–518, 1984.MathSciNetCrossRefGoogle Scholar
  53. [53]
    Zak S. H., Lee E. B., Lu W. S., “Realizations of 2-D filters and time delay systems”, IEEE Trans on Circuits and Systems, Vol. CAS-33, No. 12, 1241–1244, 1986.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • K. Galkowski
    • 1
    • 2
  • A. Kummert
    • 3
  1. 1.Institute of Control and Computation EngineeringUniversity of Zielona GoraZielona GoraPoland
  2. 2.Electrical, Information and Media EngineeringUniversity of WuppertalWuppertal
  3. 3.Faculty of Electrical, Information and Media EngineeringUniversity of WuppertalWuppertalGermany

Personalised recommendations