IEEE Trans Cybern. 2020 Mar;50(3):946-956. doi: 10.1109/TCYB.2018.2874273. Epub 2018 Oct 18.
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.
本文研究了一类时滞神经网络的被动性。为了得到更保守的被动性准则，通过考虑二阶贝塞尔-勒让德不等式，引入了两个具有时滞相关矩阵的李雅普诺夫-克拉索夫斯基泛函（LKFs）。在一个 LKF 中，系统状态向量通过时滞相关矩阵与从二阶贝塞尔-勒让德不等式继承的向量相耦合，而在另一个 LKF 中不存在这种耦合。这两个 LKFs 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 LKF 导数中出现的时变延迟的平方，得到了一些时滞相关的被动性准则。通过数值模拟，发现：1）与非耦合 LKF 相比，耦合 LKF 更有利于降低所得到的被动性准则的保守性；2）采用凸方法的被动性准则可以提供比采用非凸方法更大的延迟上界。
