Stabilization and Synchronization of Dynamical Networks
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.
- 96.J. Lu, Z. Wang, J. Cao, Pinning impulsive stabilization of nonlinear dynamical networks with time-varying delay. Int. J. Bifurcation Chaos 22(7), 1250176 (12 pp.) (2012)Google Scholar
- 97.F.R.T. Luiz, E.N.M. Elbert, Hybrid pinning control for complex networks. Int. J. Bifurcation Chaos 22(10), Article ID 1250252 (2012)Google Scholar
- 159.K. Zhang, X. Liu, Global exponential stability of nonlinear impulsive discrete systems with time delay, in The Proceedings of the 25th Chinese Control and Decision Conference, 25–27 May 2013, Guiyang, pp. 148–153 (2013)Google Scholar