Abstract A generalization of real-, complex-, and quaternion-valued neural networks is represented by matrix-valued neural networks (MVNNs), for which the states and weights are matrices. The dissipativity of impulsive MVNNs with leakage delay and mixed delays is studied in this paper, by giving sufficient criteria expressed in terms of real-valued linear matrix inequalities. After decomposing the MVNNs into real-valued systems, Lyapunov–Krasovskii functionals with double, triple, and quadruple integral terms are formulated. Also, the free weighting matrix method, simple, double, and triple Jensen inequalities, the reciprocally convex combination inequality, and the Wirtiger-based integral inequality are used to establish the sufficient criteria. Two numerical examples illustrate the feasibility and correctness of the proposed theoretical results.

中文翻译：

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具有泄漏延迟和混合延迟的脉冲矩阵值神经网络的耗散性

摘要 实值、复值和四元数值神经网络的泛化由矩阵值神经网络 (MVNN) 表示，其状态和权重是矩阵。本文通过给出以实值线性矩阵不等式表示的足够标准，研究了具有泄漏延迟和混合延迟的脉冲 MVNN 的耗散性。在将 MVNN 分解为实值系统后，制定了具有二重、三重和四重积分项的 Lyapunov-Krasovskii 泛函。此外，使用自由加权矩阵方法、简单、双重和三重 Jensen 不等式、互凸组合不等式和基于 Wirtiger 的积分不等式来建立充分准则。两个数值例子说明了所提出的理论结果的可行性和正确性。