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Stabilization and Synchronization of Dynamical Networks

  • 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 studies stabilization and synchronization problems of dynamical networks (DNs) under pinning impulsive control. Throughout this chapter, a pinning algorithm is incorporated with the impulsive control approach. In Section 6.1, stabilization of time-delay neural networks is studied. Subsection 6.1.2 proposes a delay-dependent pinning impulsive controller to stabilize the neural networks with time-delay and sufficient conditions for stabilization are presented. The obtained results show that the delay-dependent pinning impulsive controller can successfully stabilize the time-delay neural networks. However, the pinning impulsive controller depends on the network states at both impulsive instants and history times, that is, the contributions of time-delay states to the stabilization or synchronization processes can not be observed explicitly. Therefore, Subsection 6.1.3 discusses a type of pinning impulsive controllers relies only on the network states at history moments (not on the states at each impulsive instant). Results show that the proposed pinning impulsive controller can effectively stabilize the network even though only states at history moments are available to the pinning controller at each impulsive instants. In Section 6.1, only discrete delays are considered in the impulsive controllers. Then we further consider pinning impulsive controllers with both discrete and distributed time-delay effects, in Section 6.2, to synchronize the drive and response systems modeled by globally Lipschitz time-delay systems. All the theoretical results are illustrated by numerical simulations, accordingly.

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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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