Stability of Discrete-Time Impulsive Systems with Time-Delay

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


In this chapter, discrete-time impulsive systems with time-delay are presented and studied. The mechanism of impulsive control for discrete-time systems are introduced, and the concept of exponential stability for discrete-time impulsive time-delay systems is formulated. By using Lyapunov-Razumikhin technique and the method of Lyapunov functionals, several exponential stability results are constructed which can be applied to design appropriate impulsive controllers to stabilize unstable discrete-time delay systems, while some results are established that provide robustness analysis criteria for stable systems subject to impulsive perturbations.


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Copyright information

© 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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