This paper studies the problem of $H_{\infty }$ performance analysis for delayed Markovian jump neural networks (MJNNs). Firstly, the third-order Bessel–Legendre (B-L) integral inequality based on reciprocally convex approach is derived, which contains some existing ones as its special cases. Secondly, in order to facilitate the use of more information about time delays, the Lyapunov–Krasovskii functional (LKF) with delay-product-type terms is proposed. As a result, by utilizing the LKF with delay-product-type terms and the third-order B-L integral inequality based on reciprocally convex approach, less conservative sufficient conditions that guarantee the $H_{\infty }$ performance for delayed MJNNs are obtained. Finally, simulation results are given to illustrate the effectiveness of the proposed method.

本文研究的问题是 $H_{\infty }$延迟马尔可夫跳跃神经网络 (MJNN) 的性能分析。首先，推导了基于互凸方法的三阶 Bessel-Legendre (BL) 积分不等式，其中包含一些现有的不等式作为其特例。其次，为了便于使用更多关于时间延迟的信息，提出了具有延迟积类型项的 Lyapunov-Krasovskii 泛函 (LKF)。因此，通过利用具有延迟积类型项的 LKF 和基于互反凸方法的三阶 BL 积分不等式，不太保守的充分条件保证了$H_{\infty }$获得延迟 MJNN 的性能。最后，给出了仿真结果来说明所提出方法的有效性。