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Stability analysis of complex-valued impulsive systems with time delay

Author

Listed:
  • Zeng, Xu
  • Li, Chuandong
  • Huang, Tingwen
  • He, Xing

Abstract

In this paper, the global exponential stability of complex-valued impulsive systems is addressed. Some new sufficient conditions are obtained to guarantee the global exponential stability by the Lyapunov–Razumikhin theory, which extend and improve most of recent results. Moreover, the obtained Razumikhin conditions are very simple and efficient to verify in real problems and helpful to investigate the stability of delayed neural networks and synchronization problems of chaotic systems under impulsive perturbation. Finally, a numerical example is given to show the effectiveness of the obtained results.

Suggested Citation

  • Zeng, Xu & Li, Chuandong & Huang, Tingwen & He, Xing, 2015. "Stability analysis of complex-valued impulsive systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 75-82.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:75-82
    DOI: 10.1016/j.amc.2015.01.006
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    References listed on IDEAS

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    1. Wan, Xiaojun & Sun, Jitao, 2011. "Adaptive–impulsive synchronization of chaotic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1609-1617.
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    5. Xia, Yonghui & Huang, Zhenkun & Han, Maoan, 2008. "Existence and globally exponential stability of equilibrium for BAM neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 588-597.
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    Cited by:

    1. Li, Xiaodi & Shen, Jianhua & Rakkiyappan, R., 2018. "Persistent impulsive effects on stability of functional differential equations with finite or infinite delay," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 14-22.
    2. Zhang, Lei & Song, Qiankun & Zhao, Zhenjiang, 2017. "Stability analysis of fractional-order complex-valued neural networks with both leakage and discrete delays," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 296-309.
    3. Kumar, Ankit & Das, Subir & Yadav, Vijay K. & Rajeev,, 2021. "Global quasi-synchronization of complex-valued recurrent neural networks with time-varying delay and interaction terms," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Shi, Yanchao & Cao, Jinde & Chen, Guanrong, 2017. "Exponential stability of complex-valued memristor-based neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 222-234.
    5. Li, Xiaodi & Deng, Feiqi, 2017. "Razumikhin method for impulsive functional differential equations of neutral type," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 41-49.
    6. Wang, Pengfei & Zou, Wenqing & Su, Huan, 2019. "Stability of complex-valued impulsive stochastic functional differential equations on networks with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 338-354.
    7. Yang, Ni & Gao, Ruiyi & Su, Huan, 2022. "Stability of multi-links complex-valued impulsive stochastic systems with Markovian switching and multiple delays," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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