Elimination of Anticipation of a Class of Singular 2D Roesser Models by State Feedbacks

  • T. Kaczorek


Necessary and sufficient conditions for the anticipation of a class of singular 2D Roesser models are established. Two methods of elimination of the anticipation of the model by suitable choice of feedback gain matrices are proposed. The methods are illustrated by numerical examples.

Key Words

anticipation elimination existence singular 2D Roesser model state feedback 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. Dai, Singular Control Systems. Lectures Note in Control and Information Sciences, 1989, Springer-VerlagGoogle Scholar
  2. 2.
    D.M. Dubois, “Computational Derivation of Quantum Relativist Electromagnetic Systems with Forward-Backward Space–Time Shifts,” in CP517, Computing Anticipatory Systems: CAYS-Third International Conference, ed. D.M. Daniel, The American Institute of Physics, 2000, pp. 417–429Google Scholar
  3. 3.
    D.M. Dubois, “Computing Anticipatory Systems with Incursion and Hyperincursion,” in CP437, Computing Anticipatory Systems: CAYS-First International Conference, ed. D.M. Dubois, The American Institute of Physics, 1998, pp. 3–28Google Scholar
  4. 4.
    D.M. Dubois, Incursive Anticipatory Control of a Chaotic Robot Arm., in CP437, Computing Anticipatory Systems: CAYS-Third International Conference, ed. D.M. Dubois, The American Institute of Physics, 1998, pp. 406–417Google Scholar
  5. 5.
    Gałkowski, K. 2001State-Space Realizations of Linear Systems with Extensions to the General nD (n>2) CaseSpringer-VerlagLondonGoogle Scholar
  6. 6.
    Fornasini, E., Marchesini, G. 1976State-Space Realization Theory of Two-Dimensional FiltersIEEE Transactions on Automatic ControlAC-21484491Google Scholar
  7. 7.
    Fornasini, E., Marchesini, G. 1978Doubly-Indexed Dynamical Systems: State-Space Models and Structural PropertiesMathematical System Theory125972Google Scholar
  8. 8.
    Gatmacher, F.R. 1959Theory of MatricesChelseaNew YorkGoogle Scholar
  9. 9.
    Kaczorek, T. 2001Anticipatory 1D and 2D Linear SystemsInternational Journal of Computing Anticipatory Systems8319325Google Scholar
  10. 10.
    T. Kaczorek, “Elimination of Anticipation of Singular Linear Systems,” International Journal of Computing Anticipatory Systems, vol. 9, 2001 (in press)Google Scholar
  11. 11.
    T. Kaczorek, “Elimination of Anticipation of Singular 2D Roesser Model,” in Proceedings of the Fifteenth International Symposium on Mathematical Theory of Networks and Systems, Notre Dame, USA, August 12–16, 2002Google Scholar
  12. 12.
    Kaczorek, T. 1992Linear Control SystemsWileyNew YorkGoogle Scholar
  13. 13.
    Kaczorek, T. 1996Reachability and Controllability of Non-Negative 2-D Roesser Type ModelsBull. Acad. Pol. Sci. Ser. Sci. Techn.44,405410Google Scholar
  14. 14.
    Kaczorek, T. 1985Two-Dimensional Linear SystemsSpringer-VerlagBerlinGoogle Scholar
  15. 15.
    Kaczorek, T. 1988Singular General Model of 2-D Systems and its SolutionIEEE Transactions on Automatic ControlAC-33,10601061Google Scholar
  16. 16.
    T. Kaczorek, Singular 2-D continuous-discrete linear systems, Dynamics of continuous, discrete and impulse systems, Advances in Systems Science and Applications, 1995, pp. 103–108Google Scholar
  17. 17.
    Klamka, J. 1991Controllability of Dynamical SystemsKluwer Academic PublicationsDordrechtGoogle Scholar
  18. 18.
    Kurek, J. 1985The General State-Space Model for a Two-Dimensional Linear Digital SystemIEEE Transactions on Automatic ControlAC-30600602Google Scholar
  19. 19.
    Roesser, R.B. 1975A Discrete State Space Model for Linear Image ProcessingIEEE Transactions on Automatic ControlAC-20110Google Scholar
  20. 20.
    R. Rosen, Anticipatory Systems, Pergamon Press, 1985Google Scholar
  21. 21.
    Valcher, M.E. 1997On the Internal Stability and Asymptotic Behavior of 2-D Positive SystemsIEEE Transactions on Circuits and Systems - I44,602613Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Warsaw Technical University, Faculty of Electrical EngineeringInstitute of Control and Industrial ElectronicsWarszawaPoland

Personalised recommendations