This work analyzes the passivity for a set of Markov jumping reaction-diffusion neural networks limited by time-varying delays under Dirichlet and Neumann boundary conditions, respectively, in which Markov jumping is used to describe the variations among system parameters. To overcome some difficulties originated from partial differential terms, the Lyapunov–Krasovskii functional that introduces a new integral term is proposed and some inequality techniques are also adopted to obtain the delay-dependent stability conditions in terms of linear matrix inequalities, which ensures that the designed neural networks satisfy the specified performance of passivity. Finally, the advantages and effectiveness of the obtained results are verified via displaying two illustrated examples.

中文翻译：

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不同边界条件下马氏跳跃时滞反应扩散神经网络的无源性分析

这项工作分析了分别在Dirichlet和Neumann边界条件下受时变时滞限制的一组Markov跳跃反应扩散神经网络的无源性，其中使用Markov跳跃描述系统参数之间的变化。为了克服由偏微分项引起的一些困难，提出了引入新积分项的Lyapunov–Krasovskii泛函，并且还采用了一些不等式技术来获得关于线性矩阵不等式的时滞相关稳定性条件，从而确保了设计神经网络满足指定的被动性能。最后，通过显示两个示例来验证所获得结果的优势和有效性。