为了更精确地获得具有反应扩散项的时滞忆阻神经网络的状态信息,设计了一个H∞状态估计器。首先,基于Lyapunov-Krasovskii(L-K)泛函方法,构造了新的时滞乘积型增广L-K泛函来处理时变时滞带来的影响。然后,通过利用自由权矩阵、Wirtinger积分不等式、改进逆凸矩阵不等式等方法进一步降低所得结果的保守性。同时,使用Dirichlet边界条件、Green公式等来处理系统中存在的反应扩散项;最终,给出误差系统全局渐近稳定且满足特定H∞性能指标的充分条件。在此基础上,以线性矩阵不等式的形式给出状态估计器的设计方法。最后,通过数值仿真验证所设计的H∞状态估计器的有效性。
In order to obtain the state information of delayed memristive neural networks with reaction-diffusion terms more accurately, this paper designs a H∞ state estimator. Firstly, based on the Lyapunov-Krasovskii (L-K) functional method, a new delay-product-type augmented L-K functional is constructed to handle the effects of time-varying delays. Then, by utilizing techniques such as free-weight-matrix method, Wirtinger-based integral inequality, and extended reciprocally convex matrix inequality, further reduction in conservatism of the obtained results is achieved. Meanwhile, Dirichlet boundary conditions and Green formula, among others, are employed to address the reaction-diffusion terms of the system; finally, sufficient conditions for the global asymptotic stability of the error system that meet specific H∞ performance criteria are provided. Building upon this foundation, we present a design methodology for state estimator in terms of linear matrix inequalities. Finally, a numerical example is given to verify the effectiveness of the proposedH∞state estimator.
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