Exponential Stability of Impulsive Time-Delay Systems on Time Scales

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


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.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

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

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