Finite-Dimensional Dynamical Systems: Specialized Results

  • Anthony N. Michel
  • Ling Hou
  • Derong Liu
Part of the Systems&Control: Foundations&Applications book series (SCFA)


Unstable Manifold Stable Manifold Fundamental Matrix Negative Real Part Positive Real Part 
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  1. 1.
    P. J. Antsaklis and A. N. Michel, Linear Systems, Boston: Birkhäauser, 2006.Google Scholar
  2. 2.
    E. A. Barbashin and N. N. Krasovskii, “On the stability of motion in the large,”Dokl. Akad. Nauk., vol. 86, pp. 453–456, 1952.MATHGoogle Scholar
  3. 3.
    M. Fiedler and V. Ptak, “On matrices with nonpositive off-diagonal elements and positive principal minors,” Czechoslovak Math. J., vol. 12, pp. 382–400, 1962.MathSciNetGoogle Scholar
  4. 4.
    L. T. Grujić, A. A. Martynyuk, and M. Ribbens-Pavella, Large Scale Systems Under Structural and Singular Perturbations, Berlin: Springer-Verlag, 1987.Google Scholar
  5. 5.
    W. Hahn, Stability of Motion, Berlin: Springer-Verlag, 1967.MATHGoogle Scholar
  6. 6.
    J. K. Hale, Ordinary Differential Equations, New York: Wiley, 1969.MATHGoogle Scholar
  7. 7.
    H. K. Khalil, Nonlinear Systems, New York: Macmillan, 1992.MATHGoogle Scholar
  8. 8.
    N. N. Krasovskii, Stability of Motion, Stanford, CA: Stanford University Press, 1963.MATHGoogle Scholar
  9. 9.
    V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, vol. I and vol. II, New York: Academic Press, 1969.Google Scholar
  10. 10.
    J. P. LaSalle, “The extent of asymptotic stability,” Proc. Nat. Acad. Sci., vol. 48, pp. 363–365, 1960.CrossRefMathSciNetGoogle Scholar
  11. 11.
    J. P. LaSalle, The Stability and Control of Discrete Processes, New York: Springer-Verlag, 1986.MATHGoogle Scholar
  12. 12.
    J. P. LaSalle and S. Lefschetz, Stability by Liapunov’s Direct Method, New York: Academic Press, 1961.Google Scholar
  13. A. M. Liapounoff, “Problème générale de la stabilité de mouvement,” Annales de la Faculté des Sciences de l’Université de Toulouse, vol. 9, pp. 203–474, 1907. (Translation of a paper published in Comm. Soc. Math., Kharkow, 1892, reprinted in Ann. Math. Studies, vol. 17, Princeton, NJ: Princeton, 1949.)Google Scholar
  14. 14.
    A. N. Michel and C. J. Herget, Algebra and Analysis for Engineers and Scientists, Boston, Birkhäauser, 2007.Google Scholar
  15. 15.
    A. N. Michel and R. K. Miller, Qualitative Analysis of Large Scale Dynamical Systems, New York: Academic Press, 1977.MATHGoogle Scholar
  16. 16.
    A. N. Michel, K.Wang, and B. Hu, Qualitative Theory of Dynamical Systems-The Role of Stability Preserving Mappings, 2nd Edition, New York: Marcel Dekker, 2001.MATHGoogle Scholar
  17. 16a.
    R. K. Miller and A. N. Michel, “Asymptotic stability of systems: Results involving the system topology,” SIAM J. Optim. Control, vol. 18, pp. 181– 190, 1980.MATHCrossRefMathSciNetGoogle Scholar
  18. 17.
    R. K. Miller and A. N. Michel, Ordinary Differential Equations, New York: Academic Press, 1982.MATHGoogle Scholar
  19. 18.
    D. D. Siljak, Large-Scale Dynamical Systems: Stability and Structure, New York: North Holland, 1978.Google Scholar
  20. 19.
    M. Vidyasagar, Nonlinear Systems Analysis, Englewood Cliffs, NJ: Prentice Hall, 1993.MATHGoogle Scholar
  21. 20.
    T. Yoshizawa, Stability Theory by Liapunov’s Second Method, Tokyo: Math. Soc. of Japan, 1966.Google Scholar
  22. 21.
    V. I. Zubov, Methods of A. M. Lyapunov and Their Applications, Amsterdam: Noordhoff, 1964.Google Scholar

Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • Anthony N. Michel
    • 1
  • Ling Hou
    • 2
  • Derong Liu
    • 3
  1. 1.Department of Electrical EngineeringUniversity of Notre DameNotre DameU.S.A
  2. 2.Department of Electrical and Computer EngineeringSt. Cloud State UniversitySt. CloudU.S.A
  3. 3.Department of Electrical and Computer EngineeringUniversity of Illinois at ChicagoChicagoU.S.A

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