Stability in Terms of Two Measures of Impulsive 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 studies stability problems in terms of two measures for a class of nonlinear impulsive systems on time scales. First, impulsive systems on time scales are introduced and formulated in Section 8.1. In Section 8.2, several stability criteria in terms of two measures are derived for nonlinear impulsive systems on time scales, by establishing a new comparison result. As applications, nonlinear impulsive control problems of continuous and discrete chaotic systems are discussed. Some nonlinear impulsive stabilization criteria are obtained where both nonuniform and uniform impulsive intervals are considered. Four examples are discussed to illustrate the effectiveness of the theoretical results and the proposed impulsive control schemes. Section 8.3 presents various stability and instability results by Lyapunov direct method.


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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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