This paper is concerned with passivity of a class of delayed neural networks. In order to derive less conservative passivity criteria, two Lyapunov–Krasovskii functionals (LKFs) with delay-dependent matrices are introduced by taking into consideration a second-order Bessel–Legendre inequality. In one LKF, the system state vector is coupled with those vectors inherited from the second-order Bessel–Legendre inequality through delay-dependent matrices, while no such coupling of them exists in the other LKF. These two LKFs are referred to as the coupled LKF and the noncoupled LKF, respectively. A number of delay-dependent passivity criteria are derived by employing a convex approach and a nonconvex approach to deal with the square of the time-varying delay appearing in the derivative of the LKF. Through numerical simulation, it is found that: 1) the coupled LKF is more beneficial than the noncoupled LKF for reducing the conservatism of the obtained passivity criteria and 2) the passivity criteria using the convex approach can deliver larger delay upper bounds than those using the nonconvex approach.

中文翻译：

---

基于Lyapunov-Krasovskii泛函的时滞相关矩阵的时滞神经网络的无源性分析

本文涉及一类延迟神经网络的无源性。为了得出较不保守的无源性准则，通过考虑二阶贝塞尔-勒让德不等式，引入了两个具有时延依赖矩阵的Lyapunov-Krasovskii泛函（LKF）。在一个LKF中，系统状态向量通过依赖于延迟的矩阵与从二阶Bessel-Legendre不等式继承的向量耦合，而在另一个LKF中不存在这样的耦合。这两个LKF分别称为耦合LKF和非耦合LKF。通过采用凸方法和非凸方法来处理出现在LKF导数中的时变延迟的平方，可以得出许多与延迟有关的无源性准则。通过数值模拟，发现：