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Complete Type Lyapunov-Krasovskii Functionals

  • Vladimir L. Kharitonov
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 38)

Abstract

In this chapter we give a general description of the complete type quadratic Lyapunov-Krasovskii functionals. Special Lyapunov matrices associated with the functionals are also defined. Uniqueness conditions, as well as a numerical scheme for computation of the Lyapunov matrices, are discussed. Some robust stability conditions. based on the functional, close the chapter. All main results are illustrated with numerical examples.

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References

  1. 1.
    Bellman R.E. and K.L. Cooke (1963) Differential-Difference Equations, Academic Press New YorkzbMATHGoogle Scholar
  2. 2.
    Datko R. (1972) An algorilhm for computing Liapunov funClionals for some differential-difference equations. In Ordinary Differential Equations. NRL-MRC Conference, Academic Press New York, 387–398Google Scholar
  3. 3.
    Niculescu S.-I.E.I. Verriest Dugard L. and J.-M. Dion. (1997) Stability and Robust Stability of Time-Delay Systems: A Guided Tour. In Stability and Control of Time Delay Systems, Dugard L. E.L Verriest (eds). Lecture NOles in Control and Information Sciences, Springer Verlag London, 228: 1–71Google Scholar
  4. 4.
    Infante E.F. and W.B. Castelan (1978) A Liapunov functional for a matrix difference-differential equation. Journal of Diffcrential Equations, 29:439–451MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Hale J.K. and S. M. Verduyn Lunel (1993) Introduction to Functional Differential Equations. Springer-Verlag New YorkzbMATHGoogle Scholar
  6. 6.
    Huang W. (1989) Generalization of Liapunov’s theorem in a linear delay system. Journal of Mathematical Analysis and Applications, 142:83–94MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Kharitonov V.L. and A.P. Zhabko (2003) Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems. Automatica, 39:15–20MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Kharitonov Y.L. (1999) Robust stability analysis of time delay systems: A survey. Annual Reviews in Control, 23:185–196Google Scholar
  9. 9.
    Krasovskii N. N. (1956) On the application of the second method of Lyapunov for equations with time delays. Prikl. Mat. Mech., 20:315–327 (in Russian)MathSciNetGoogle Scholar
  10. 10.
    Louisell. J. (1997) Numerics of the stability exponent and eigenvalue abscissas of a matrix delay system. In Stability and Control of Time-Delay Systems, Dugard L. E.I. Verriest, (eds), Lecture Notes in Control and Information Sciences, Springer Verlag London, 228: 140–157Google Scholar
  11. 11.
    Repin Yu.M. (1965), Quadratic Liapunov functionals for systems with delay, Prikl. Mat. Mech., 29:564–566 (in Russian)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Vladimir L. Kharitonov
    • 1
  1. 1.Department of Automatic ControlC1NVESTAV- IPNMexicoMexico

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