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Local synchronization of nonlinear dynamical networks with hybrid impulsive saturation control inputs

Author

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  • He, Zhilong
  • Li, Chuandong
  • Li, Yi
  • Cao, Zhengran
  • Zhang, Xiaoyu

Abstract

Under the hybrid impulsive control with actuator saturations, this paper studies the local synchronization problem of a class of nonlinear dynamical networks. However, the discontinuity caused by the impulsive effect and the saturation nonlinearity caused by the actuator saturation have brought great challenge to the theoretical analysis of such problems. Firstly, this paper uses mathematical induction to estimate the admissible set of the system state at the impulse instant, which is used to ensure that the saturation nonlinear problem can be dealt with by the sector nonlinear model method and the polyhedral representation method. Secondly, by constructing a suitable time-dependent Lyapunov-Krasovsknii functional (LKF), using Jensen’s inequality, Wirtinger-based inequality and the sector nonlinearity model approach, a sufficient condition has been derived, which guarantee the exponential stability of the synchronization error system in terms of linear matrix inequalities (LMIs). Thirdly, some synchronization criteria are obtained by using polytopic representation approach to deal with the saturation nonlinearity. Based on these criteria, the saturated impulsive and sampled-data controller is designed, and the region of attraction of the drive response error system is estimated. As a corollary, exponentially synchronization conditions and controller design are also presented for the nonlinear dynamical networks without actuator saturation. Finally, two numerical examples shows the effectiveness of the obtained results.

Suggested Citation

  • He, Zhilong & Li, Chuandong & Li, Yi & Cao, Zhengran & Zhang, Xiaoyu, 2021. "Local synchronization of nonlinear dynamical networks with hybrid impulsive saturation control inputs," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    • Handle: RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005415
    DOI: 10.1016/j.amc.2021.126452
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    References listed on IDEAS

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    1. Wang, Jun & Shi, Kaibo & Huang, Qinzhen & Zhong, Shouming & Zhang, Dian, 2018. "Stochastic switched sampled-data control for synchronization of delayed chaotic neural networks with packet dropout," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 211-230.
    2. Lee, S.H. & Selvaraj, P. & Park, M.J. & Kwon, O.M., 2020. "Improved results on H∞ stability analysis of sampled-data systems via looped-functionals and zero equalities," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    3. He, Zhilong & Li, Chuandong & Li, Hongfei & Zhang, Qiangqiang, 2020. "Global exponential stability of high-order Hopfield neural networks with state-dependent impulses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
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