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Hybrid stabilization and synchronization of nonlinear systems with unbounded delays

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  • Liu, Xinzhi
  • Stechlinski, Peter

Abstract

The stabilization of nonlinear systems with bounded and unbounded time-delays via hybrid control is studied. We investigate and identify switching rules for which stabilization can be verified a priori. When this approach is inadequate, stabilizing state-dependent switching rules are constructed. This method is based on partitioning the state-space into switching regions. Unwanted physical behavior, such as chattering and Zeno behavior, is avoided. Sufficient conditions are established using Razumikhin-like theorems. The theoretical results provide insight into how hybrid control strategies can be constructed to synchronize a class of nonlinear systems with unbounded delay. The findings are illustrated through numerical simulations.

Suggested Citation

  • Liu, Xinzhi & Stechlinski, Peter, 2016. "Hybrid stabilization and synchronization of nonlinear systems with unbounded delays," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 140-161.
    • Handle: RePEc:eee:apmaco:v:280:y:2016:i:c:p:140-161
    DOI: 10.1016/j.amc.2016.01.023
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    References listed on IDEAS

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    1. Li, Ping & Zhong, Shou-Ming & Cui, Jin-Zhong, 2009. "Stability analysis of linear switching systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 474-480.
    2. Li, Ping & Cao, Jinde & Wang, Zidong, 2007. "Robust impulsive synchronization of coupled delayed neural networks with uncertainties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 261-272.
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    Cited by:

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    2. Zeng, Deqiang & Zhang, Ruimei & Liu, Yajuan & Zhong, Shouming, 2017. "Sampled-data synchronization of chaotic Lur’e systems via input-delay-dependent-free-matrix zero equality approach," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 34-46.
    3. Zhai, Shidong & Zhou, Yuan & Li, Qingdu, 2017. "Synchronization for coupled nonlinear systems with disturbances in input and measured output," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 227-237.

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