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Non-fragile dissipative state estimation for semi-Markov jump inertial neural networks with reaction-diffusion

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  • Sun, Lin
  • Su, Lei
  • Wang, Jing

Abstract

In this paper, the non-fragile dissipative state estimation is addressed for semi-Markov jump inertial neural networks with reaction-diffusion. A semi-Markov jump model is used to describe the stochastic jump parameters in networks. Different from the invariable transition probabilities in the traditional Markov jump systems, the transition probabilities of the semi-Markov jump systems rely on the stochastic sojourn-time. Accordingly, the Weibull distribution taking the place of the exponential distribution in this paper is adopted for the sojourn-time of each mode in the system. Firstly, by utilizing an applicable vector substitution, the second-order differential system could be converted into the first-order one. Afterwards, via constructing a seemly Lyapunov function of the semi-Markov inertial neural networks and adequately taking advantage of the peculiarities of cumulative distribution functions, some sufficient conditions with less conservatism are constructed to assure that the estimation error system is strictly (R1,R2,R3)−ϱ−dissipative stochastically stable. Based on these conditions, mode-dependent estimator gains are designed. Finally, a numerical example is proposed to validate the availability of the provided approach.

Suggested Citation

  • Sun, Lin & Su, Lei & Wang, Jing, 2021. "Non-fragile dissipative state estimation for semi-Markov jump inertial neural networks with reaction-diffusion," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    • Handle: RePEc:eee:apmaco:v:411:y:2021:i:c:s0096300321004938
    DOI: 10.1016/j.amc.2021.126404
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    References listed on IDEAS

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    1. Wang, Yuxiao & Cao, Yuting & Guo, Zhenyuan & Huang, Tingwen & Wen, Shiping, 2020. "Event-based sliding-mode synchronization of delayed memristive neural networks via continuous/periodic sampling algorithm," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    2. Song, Xiaona & Men, Yunzhe & Zhou, Jianping & Zhao, Junjie & Shen, Hao, 2017. "Event-triggered H∞ control for networked discrete-time Markov jump systems with repeated scalar nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 123-132.
    3. Lu, Jun Guo, 2008. "Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 116-125.
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    Cited by:

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    2. Zhang, Hai & Chen, Xinbin & Ye, Renyu & Stamova, Ivanka & Cao, Jinde, 2023. "Adaptive quasi-synchronization analysis for Caputo delayed Cohen–Grossberg neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 49-65.
    3. Zhang, Ziwei & Chen, Zongjie & Sheng, Zhang & Li, Dan & Wang, Jing, 2022. "Static output feedback secure synchronization control for Markov jump neural networks under hybrid cyber-attacks," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    4. Xiong, Kailong & Hu, Cheng & Yu, Juan, 2023. "Direct approach-based synchronization of fully quaternion-valued neural networks with inertial term and time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    5. Yaning Yu & Ziye Zhang, 2022. "State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays," Mathematics, MDPI, vol. 10(10), pages 1-14, May.
    6. Mei, Yu & Wang, Guanqi & Shen, Hao, 2023. "Adaptive Event-Triggered L2−L∞ Control of Semi-Markov Jump Distributed Parameter Systems," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    7. Liang, Tiantian & Shi, Shengli & Ma, Yuechao, 2023. "Asynchronous sliding mode control of continuous-time singular markov jump systems with time-varying delay under event-triggered strategy," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    8. Karnan, A. & Nagamani, G., 2022. "Non-fragile state estimation for memristive cellular neural networks with proportional delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 217-231.

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