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4. Stability and stabilization

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Two-Dimensional Linear Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 68))

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References

  1. Agathoklis P., Jury E.I., Mansour M.: The margin of stability of 2-D linear discrete systems. IEEE Trans. Acoustics, Speech, Signal Processing vol. ASSP-30, no.6, 1982, pp.869–873.

    Google Scholar 

  2. Ahmed A.R.E.: On the stability of two-dimensional discrete systems. IEEE Trans. Autom. Control vol. AC-25, no.3, 1980, pp.551–552.

    Google Scholar 

  3. Basu S., Bose N.K.: Stability of 2-D matrix rational approximants from input data. IEEE Trans. Autom. Control vol. AC-26, no.2, 1981, pp.540–541.

    Google Scholar 

  4. Chiasson J.N., Brierly S.D.: New stability tests for 2-D polynomials. Transactions CDC 1984 /in press/

    Google Scholar 

  5. Davis D.L.: A correct proof of Huang's theorem. IEEE Trans. Acoustics, Speech, Signal Processing, October 1976, pp.425–426.

    Google Scholar 

  6. DeCarlo R.A., Murray J., Sacks R.: Multivariable Nyquist theory. Int. J. Control vol.25, no.5, 1977, pp.657–675.

    Google Scholar 

  7. Delsarte Ph., Genin Y.V., Kamp Y.G.: A simple proof of Rudin's multivariable stability theorem. IEEE Acoustics, Speech, Signal Processing vol. ASSP-28, no.6, 1980, pp.701–705.

    Google Scholar 

  8. Eising R.: 2-D Systems; An Algebraic Approach. Mathematish Centrum, Amsterdam 1979.

    Google Scholar 

  9. Fornasini E., Marchesini G.: Doubly — indexed dynamical systems;: State — space models and structural properties. Mathematical Systems Theory vol.12, 1978, pp.59–72.

    Google Scholar 

  10. Fornasini E., Marchesini G.: On the internal stability of two-dimensional filters. IEEE Trans. Autom. Control vol. AC-24, 1979, pp.129–130.

    Google Scholar 

  11. Fornasini E., Marchesini G.: Stability analysis od 2-D systems. IEEE Trans. Circuits, Systems vol. CAS-27, 1980, pp.1210–1217.

    Google Scholar 

  12. Goodman D.: An alternate proof of Huang's theorem. IEEE Trans. Acoustics, Speech, Signal Processing, Oct. 1976, pp.426–427.

    Google Scholar 

  13. Goodman D.: Some stability properties of two-dimensional linear shift — invariant digital filters. IEEE Trans. Circuits Syst. vol. CAS-24, no.4, 1977, pp.201–208.

    Google Scholar 

  14. Hormander L.: An Introduction to Complex Analysis in Several Variables. North-Holland 1973.

    Google Scholar 

  15. Huang T.S.: Stability of two-dimensional recursive filters. IEEE Trans. Audio Electroacoust. vol. AU-20, no.2, 1972, pp.158–163.

    Google Scholar 

  16. Jury E.I., Mansour M.: A set of necessary and sufficient stability conditions for low order two-dimensional polynomials. IEEE Trans. Autom. Control vol. AC-27, no.1, 1982, pp.192–194.

    Google Scholar 

  17. Justice J.H., Shanks J.L.: Stability criterion for n-dimensional digital filters. IEEE Trans. Autom. Control, June 1973, pp.284–286.

    Google Scholar 

  18. Kamen E.W.: Asymptotic stability of linear shift invariant two-dimensional digital filters. IEEE Trans. Circuits, Systems vol. CAS-27, 1980, pp.1234–1240.

    Google Scholar 

  19. Kamen E.W.: On the relationship between zero criteria for two-variable polynomials and asymptotic stability of delay differential equations. IEEE Trans. Autom. Control vol. AC-25, no.5, 1980.

    Google Scholar 

  20. Kurek J.E. Stabilities of 2-D linear discrete-time systems. Preprints IFAC 9th World Congress, Budapest July 2–6, 1984, pp. 150–154

    Google Scholar 

  21. Pandolfi L. Exponential stability of 2-D systems. Systems and Control Letters, vol.4, 1984, pp. 381–385

    Google Scholar 

  22. Rudin W.: Principles of Mathematical Analysis. McGraw-Hill, New York 1964.

    Google Scholar 

  23. Shanks J.L., Treitel S., Justice J.H.: Stability and synthesis of two-dimensional recursive filters. IEEE Trans. Audio Electroacoust. vol. AU-20, no.2, 1972, pp.115–128.

    Google Scholar 

  24. Strintzis M.G.: Tests of stability of multidimensional filters. IEEE Trans. Circuits Systems vol. CAS-24, no.8, 1977, pp.432–437.

    Google Scholar 

  25. Walach E., Zeheb E.: N-dimensional stability margins computation and a variable transformation. IEEE Trans. Acoustics, Speech, Signal Processing vol. ASSP-30, no.6, 1982, pp.887–893.

    Google Scholar 

  26. Wu-Sheng Lu, Lee E.B.: Stability analysis for two-dimensional systems. IEEE Trans. Circuits, Systems vol. CAS-30, no.7, 1983, pp.455–461.

    Google Scholar 

  27. Agathoklis P., Jury E, Mansour M.: Asymptotic stability and the Lyaponov equation for two-dimensional discrete systems. Preprints IFAC 9th World Congress, Budapest, July 2–6, 1984, vol. VIII, pp. 155–158

    Google Scholar 

  28. Moylan P.J.: Matrices with positive principal minors. Linear Algebra and its Applications, vol. 17, 1977, pp. 53–58.

    Google Scholar 

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Tadeusz Kaczorek

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© 1985 Springer-Verlag

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(1985). 4. Stability and stabilization. In: Kaczorek, T. (eds) Two-Dimensional Linear Systems. Lecture Notes in Control and Information Sciences, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0005621

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  • DOI: https://doi.org/10.1007/BFb0005621

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  • Print ISBN: 978-3-540-15086-2

  • Online ISBN: 978-3-540-39226-2

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