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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
9 References
Aggarwal J. K., “Principles of multidimensional wave digital filtering”, Digital Signal Processing, Ed. Fettweis A., 262–282, Point Lobo Press, Hollywood, 1979.
Amann N., Owens D.H., Rogers E., “Predictive optimal iterative learning control”, Int. J. Control, Vol. 69, No. 2, 203–226, 1998.
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.
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.
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.
Bose N.K. (Ed.), Buchberger B. (Ed.), Guiver J.P. (Ed.), “Multidimensional Systems Theory and Applications”, Kluwer Academic Pub., 2004.
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.
Buchberger B., “Ein algorithmishes kriterium fur die losbarkeit eines algebraishen gleichungsystems”, Aeq. Math., Vol. 4, 374–383, 1970.
Fettweis A., “Multidimensional wave digital filters”, European Conf. Circuit Theory and Design, Vol. II, 409–416, 1976.
Fettweis A., “Multidimensional circuits and systems”, in Proc. IEEE Int. Symp. on Circuits and Systems, Vol. 3, 951–957, 1984.
Fettweis A., “Some properties of scattering Hurwitz polynomials”, Archiv für Elektronik und Übertragungstechnik, Vol. 38, 171–176, 1984.
Fettweis A., “Wave digital filters: Theory and practice”, (invited paper) Proc. of the IEEE, Vol. 74, No. 2, 270–327, 1986.
Fettweis A., “Discrete passive modeling of physical systems described by PDEs”, European Signal Proceeding Conference, Vol. 1, 55–62, 1992.
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.
Fettweis A., Basu S., “New results on multidimensional Hurwitz polynomials”, ISCAS, Vol. 3, 1359–1362, 1985.
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.
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.
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.
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.
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.
Fornasini E., Marchesini G. “Doubly-indexed dynamical systems”, Math. Syst. Theory, Vol. 12, 59–72, 1978.
Fornasini E., “A 2-D systems approach to river pollution modelling, Multi-dimensional Systems and Signal Processing, Vol. 2, 233–265, 1991.
Fornasini E., Zampieri S., “A note on the state space realization of 2D FIR transfer functions”, Systems & Control Letters, Vol. 16, 117–122, 1991.
Fries M., “Numerical integration of Euler flow by means of multidimensional wave digital principles”, Dissertation, Ruhr-Universität Bochum, 1995.
Gałkowski K., Vinnikov V., (Ed.), “International Journal of Control, spec. issue”, 2004, Vol. 77, no 9.
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.
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.
Galkowski K., Wood J., Eds., “Multidimensional Signals, Circuits and Systems”, Taylor & Francis, 2001.
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.
Goodman D,. “Some stability properties of two-dimensional linear shift-invariant filters”, IEEE Trans. on Circuits and Systems, Vol. CAS 24, 201–208, 1977.
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.
Kaczorek, T., “Linear Control Systems”, Research Studies Press LTD, (distributed by John Wiley & Sons Inc), 1993.
Kaczorek T., “2-D continuous-discrete linear systems”, in Proc. Tenth Int. Conf. on System Eng. ICSE'94, Vol. 1, 550–557, 1994.
Kailath T., “Linear Systems”, Prentice-Hall, Englewood Cliffs, N.Y., 1980.
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.
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.
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.
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.
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.
Kummert A., “On the synthesis of multidimensional reactance multiports”, IEEE Trans. on Circuits and Systems, Vol. CAS-38, No. 6, 637–642, 1991.
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.
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.
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.
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.
Rocha P., “Structure and Representations for 2-D Systems”, PhD Thesis, University of Groningen, The Netherlands, 1990.
Roesser R., “A discrete state space model for linear image processing”, IEEE Trans. Automatic Control, vol. 20, pp. 1–10, 1975.
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.
Smyth K., “Computer aided analysis for linear repetitive processes”, PhD Thesis, University of Strathclyde, Glasgow, UK, 1992.
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.
Vollmer M., An approach to automatic generation of wave digital stzructures from PDEs, IEEE International Symposium on Circuits and Systems, 2004.
Youla D.C., Gnavi G. Notes on n dimensional systems, IEEE Trans on Circuits and Systems, Vol. CAS-26, No. 2, 105–111, 1979.
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.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this paper
Cite this paper
Galkowski, K., Kummert, A. (2005). Multidimensional Systems, Signals, Circuits, and Repetitive Processes: Theory, Applications, and Future Trends. In: Saeed, K., Pejaś, J. (eds) Information Processing and Security Systems. Springer, Boston, MA. https://doi.org/10.1007/0-387-26325-X_28
Download citation
DOI: https://doi.org/10.1007/0-387-26325-X_28
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-25091-5
Online ISBN: 978-0-387-26325-0
eBook Packages: Computer ScienceComputer Science (R0)