School of Mathematics, Anhui Polytechnic University, Wuhu 241000, PR China.
Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany; Institute of Physics, Humboldt University of Berlin, Berlin 12489, Germany.
Neural Netw. 2014 Mar;51:39-49. doi: 10.1016/j.neunet.2013.12.001. Epub 2013 Dec 9.
This paper is concerned with the global exponential stability of switched stochastic neural networks with time-varying delays. Firstly, the stability of switched stochastic delayed neural networks with stable subsystems is investigated by utilizing the mathematical induction method, the piecewise Lyapunov function and the average dwell time approach. Secondly, by utilizing the extended comparison principle from impulsive systems, the stability of stochastic switched delayed neural networks with both stable and unstable subsystems is analyzed and several easy to verify conditions are derived to ensure the exponential mean square stability of switched delayed neural networks with stochastic disturbances. The effectiveness of the proposed results is illustrated by two simulation examples.
本文研究了具有时变时滞的切换随机神经网络的全局指数稳定性。首先，利用数学归纳法、分段 Lyapunov 函数和平均驻留时间方法研究了具有稳定子系统的切换随机时滞神经网络的稳定性。其次，利用脉冲系统的扩展比较原理，分析了具有稳定和不稳定子系统的随机切换时滞神经网络的稳定性，并推导出了几个易于验证的条件，以确保具有随机干扰的切换时滞神经网络的指数均方稳定性。通过两个仿真示例验证了所提出的结果的有效性。
