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On input-to-state stability for stochastic coupled control systems on networks

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  • Gao, Shang
  • Wu, Boying

Abstract

This paper investigates the input-to-state stability (ISS) properties for stochastic coupled control systems on networks (SCCSNs). With the help of Lyapunov method and graph theory, some inequality techniques and stochastic analysis skills, some sufficient criteria are obtained for eλt-weighted integral ISS in mean and almost sure exponential ISS of SCCSNs. These sufficient criteria are closely related to the topological property of the network anatomy. Finally, an example is given to illustrate the results.

Suggested Citation

  • Gao, Shang & Wu, Boying, 2015. "On input-to-state stability for stochastic coupled control systems on networks," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 90-101.
    • Handle: RePEc:eee:apmaco:v:262:y:2015:i:c:p:90-101
    DOI: 10.1016/j.amc.2015.04.007
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    References listed on IDEAS

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    1. Stefano Allesina & Si Tang, 2012. "Stability criteria for complex ecosystems," Nature, Nature, vol. 483(7388), pages 205-208, March.
    2. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    3. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
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    Cited by:

    1. Cheng Peng & Jiaxin Ma & Qiankun Li & Shang Gao, 2022. "Noise-to-State Stability in Probability for Random Complex Dynamical Systems on Networks," Mathematics, MDPI, vol. 10(12), pages 1-11, June.
    2. Liu, Yan & Guo, Ying & Li, Wenxue, 2016. "The stability of stochastic coupled systems with time delays and time-varying coupling structure," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 507-520.
    3. Peng, Cheng & Liu, Xiaoqi & Kang, Rui & Wang, Sihan & Gao, Shang, 2023. "Stochastic input-to-state stability for stochastic complex dynamical control networks with impulsive perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    4. Rui Kang & Shang Gao, 2022. "Stabilization for Stochastic Coupled Kuramoto Oscillators via Nonlinear Distributed Feedback Control," Mathematics, MDPI, vol. 10(18), pages 1-9, September.
    5. Gao, Shang & Huang, Feifan, 2023. "Integral input-to-state stability for delayed networks control systems and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    6. Guo, Ying & Zhao, Wei & Ding, Xiaohua, 2019. "Input-to-state stability for stochastic multi-group models with multi-dispersal and time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 114-127.

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