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A new result on H∞ performance state estimation for static neural networks with time-varying delays

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  • Tian, Yufeng
  • Wang, Zhanshan

Abstract

This paper investigates the H∞ performance state estimation problem for static neural networks with time-varying delays. A parameter-dependent reciprocally convex inequality (PDRCI) is presented, which encompasses some existing results as its special cases. By dividing the estimation error of activation function into two parts, an improved Lyapunov-Krasovskii functional (LKF) is constructed, in which the slope information of activation function (SIAF) can be fully captured. Combining PDRCI and the improved LKF, a new criterion is obtained to ensure the estimation error system to be asymptotically stable with H∞ performance. By using a decoupling principle, the estimator gain matrices are solved in terms of linear matrix inequalities (LMIs). Compared with some existing works, the restrictions on slack matrices are overcome, which directly leads to performance improvement and reduction of conservativeness in the estimator solution. Two examples are illustrated to verify the advantages of the developed criterion.

Suggested Citation

  • Tian, Yufeng & Wang, Zhanshan, 2021. "A new result on H∞ performance state estimation for static neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    • Handle: RePEc:eee:apmaco:v:388:y:2021:i:c:s0096300320305129
    DOI: 10.1016/j.amc.2020.125556
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    References listed on IDEAS

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    1. Jiao, Shiyu & Shen, Hao & Wei, Yunliang & Huang, Xia & Wang, Zhen, 2018. "Further results on dissipativity and stability analysis of Markov jump generalized neural networks with time-varying interval delays," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 338-350.
    2. Wang, Zhanshan & Ding, Sanbo & Zhang, Huaguang, 2017. "Hierarchy of stability criterion for time-delay systems based on multiple integral approach," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 422-428.
    3. Michael B. Elowitz & Stanislas Leibler, 2000. "A synthetic oscillatory network of transcriptional regulators," Nature, Nature, vol. 403(6767), pages 335-338, January.
    4. Tan, Guoqiang & Wang, Zhanshan & Li, Cong, 2020. "H∞ performance state estimation of delayed static neural networks based on an improved proportional-integral estimator," Applied Mathematics and Computation, Elsevier, vol. 370(C).
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