The Z-Transform Method

  • Saber N. Elaydi
Part of the Undergraduate Texts in Mathematics book series (UTM)


In the last four chapters, we used the so-called time domain analysis. In this approach we investigate the difference equations as it is, that is without transforming it into another doman. We either find solutions of the difference equations or provide information about their qualitative behavior.


Difference Equation Asymptotic Stability Partial Fraction Fundamental Matrix Zero Solution 


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  1. [1]
    R.V. Churchill and J.W. Brown, Complex Variables and Applications, McGraw Hill, New York, 1990.Google Scholar
  2. [2]
    S. Elaydi, “Stability of Volterra Difference Equations of Convolution Type,” Proceedings of the Special Program at Nankai Institute of Mathematics, (Ed. Liao Shan-Tao et. al. ), World Scientific, Singapore, 1993, pp. 66–73.Google Scholar
  3. [3]
    S. Elaydi, “Global Stability of Difference Equations,” Proceedings of the First World Congress of Nonlinear Analysis, Florida, 1992, Kluwer (forthcoming).Google Scholar
  4. [4]
    A. Brauer, “Limits for the Characteristic Roots of a Matrix, II,” Duke Math. J., 14 (1947), 21–26.MathSciNetMATHCrossRefGoogle Scholar


  1. A main reference for the Z transform is the book by E.I. Jury, Theory and Applications of the Z-Transform Method, Robert E. Kreiger, Florida, 1982.Google Scholar
  2. J.A. Cadzow, Discrete Time Systems, Prentice Hall, New Jersey, 1973.Google Scholar
  3. K. Ogata, Discrete-Time Control Systems, Prentice Hall, New Jersey, 1987.Google Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Saber N. Elaydi
    • 1
  1. 1.Department of MathematicsTrinity UniversitySan AntonioUSA

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