Xiong Jing-Jing, Zhang Guobao
IEEE Trans Neural Netw Learn Syst. 2018 Nov;29(11):5756-5760. doi: 10.1109/TNNLS.2018.2795546. Epub 2018 Feb 12.
In this brief, the problem of delay-dependent stability of recurrent neural networks with time-varying delays is studied. A newly augmented Lyapunov-Krasovskii functional (LKF) that considers the information of the nonzero lower bound of time-varying delays is developed. Moreover, the information of the delayed state terms is not considered as elements of augmented vectors when constructing the LKF. An improved stability criterion with the framework of linear matrix inequalities is derived by employing the integral inequality and reciprocally convex combination. With the comparison to the existing ones, the developed stability criterion for neural networks has less conservatism and complexity. Finally, two widely used numerical examples are given to show the effectiveness and superiority of the obtained stability criterion.
在本简报中，研究了具有时变延迟的递归神经网络的时滞依赖稳定性问题。开发了一种新的增广Lyapunov-Krasovskii泛函（LKF），该泛函考虑了时变延迟非零下界的信息。此外，在构造LKF时，延迟状态项的信息不作为增广向量的元素。通过使用积分不等式和倒数凸组合，推导了一个具有线性矩阵不等式框架的改进稳定性准则。与现有准则相比，所开发的神经网络稳定性准则具有更少的保守性和复杂性。最后，给出了两个广泛使用的数值例子，以说明所获得的稳定性准则的有效性和优越性。
