Advertisement

Exponential Stability of Impulsive Time-Delay Systems on Time Scales

  • Xinzhi Liu
  • Kexue Zhang
Chapter
Part of the IFSR International Series in Systems Science and Systems Engineering book series (IFSR, volume 33)

Abstract

This chapter is devoted to study the exponential stability of impulsive time-delay systems on time scales. Section 9.1 introduces and formulates impulsive time-delay systems on time scales. In Section 9.2, global exponential stability is discussed and sufficient conditions are provided by using Lyapunov-Razumikhin technique. Exponential stability is studied in Section 9.3 by the method of Lyapunov functionals. Stability results presented in this chapter extend and generalize the results introduced in Chapter  2 for discrete-time impulsive systems with time-delay to impulsive time-delay systems on hybrid time domains.

References

  1. 101.
    Y. Ma, J. Sun, Stability criteria of delayed impulsive systems on time scales. Nonlinear Anal. Theory Methods Appl. 67(4), 1181–1189 (2007)CrossRefGoogle Scholar
  2. 103.
    Y. Ma, J. Sun, Stability in terms of two measures of impulsive time-delay systems on time scales. Acta Math. Sinica Chin. Ser. 51(4), 755–760 (2008)MathSciNetzbMATHGoogle Scholar
  3. 106.
    J.G. Mesquita, Measure functional differential equations and impulsive functional dynamic equations on time scales. PhD Thesis, Universidade de Sao Paulo, Sao Carlos (2012)Google Scholar
  4. 134.
    Q. Wang, X. Liu, Exponential stability for impulsive delay differential equations by Razumikhin method. J. Math. Anal. Appl. 309(2), 462–473 (2005)MathSciNetCrossRefGoogle Scholar
  5. 135.
    Q. Wang, X. Liu, Impulsive stabilization of delay differential systems via the Lyapunov – Razumikhin method. Appl. Math. Lett. 20(8), 839–845 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Xinzhi Liu
    • 1
  • Kexue Zhang
    • 1
  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada

Personalised recommendations