Huang Chuangxia, Cao Jie, Cao Jinde
College of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410114, China.
Department of Mathematics, Southeast University, Nanjing 210096, China; Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
Neural Netw. 2016 Oct;82:84-99. doi: 10.1016/j.neunet.2016.07.009. Epub 2016 Jul 26.
This paper addresses the exponential stability of switched cellular neural networks by using the mode-dependent average dwell time (MDADT) approach. This method is quite different from the traditional average dwell time (ADT) method in permitting each subsystem to have its own average dwell time. Detailed investigations have been carried out for two cases. One is that all subsystems are stable and the other is that stable subsystems coexist with unstable subsystems. By employing Lyapunov functionals, linear matrix inequalities (LMIs), Jessen-type inequality, Wirtinger-based inequality, reciprocally convex approach, we derived some novel and less conservative conditions on exponential stability of the networks. Comparing to ADT, the proposed MDADT show that the minimal dwell time of each subsystem is smaller and the switched system stabilizes faster. The obtained results extend and improve some existing ones. Moreover, the validness and effectiveness of these results are demonstrated through numerical simulations.
本文通过使用与模式相关的平均驻留时间（MDADT）方法来研究切换细胞神经网络的指数稳定性。该方法与传统的平均驻留时间（ADT）方法有很大不同，它允许每个子系统有自己的平均驻留时间。针对两种情况进行了详细研究。一种是所有子系统都是稳定的，另一种是稳定子系统与不稳定子系统共存。通过使用李雅普诺夫泛函、线性矩阵不等式（LMI）、杰森型不等式、基于 Wirtinger 的不等式、相互凸方法，我们得出了关于网络指数稳定性的一些新颖且保守性较低的条件。与 ADT 相比，所提出的 MDADT 表明每个子系统的最小驻留时间更小，并且切换系统稳定得更快。所获得的结果扩展并改进了一些现有结果。此外，通过数值模拟验证了这些结果的有效性和实用性。
