School of Electronics and Information Engineering, Soochow University, Suzhou 215006, PR China.
Neural Netw. 2012 Dec;36:136-45. doi: 10.1016/j.neunet.2012.10.002. Epub 2012 Oct 13.
This paper is concerned with the global exponential estimating problem of delayed stochastic neural networks with Markovian switching. By fully taking the inherent characteristic of such kinds of neural networks into account, a novel stochastic Lyapunov functional is constructed in which as many as possible of the positive definite matrices are dependent on the system mode and a triple-integral term is introduced. Based on it, a delay- and mode-dependent criterion is derived under which not only the neural network is mean square exponentially stable but also the decay rate is well obtained. Moreover, it is shown that the established stability condition includes some existing ones as its special cases, and is thus less conservative. This approach is then extended to two more general cases where mode-dependent time-varying delays and parameter uncertainties are considered. Finally, three numerical examples are presented to demonstrate the performance and effectiveness of the developed approach.
这篇论文研究了具有马尔可夫切换的时滞随机神经网络的全局指数估计问题。通过充分考虑这类神经网络的固有特性，构造了一个新颖的随机李雅普诺夫泛函，其中尽可能多的正定矩阵依赖于系统模式，并引入了一个三重积分项。在此基础上，得到了一个时滞和模式相关的判据，在此判据下，不仅神经网络的均方指数稳定，而且还得到了衰减率。此外，结果表明，所建立的稳定性条件包含了一些作为特例的已有条件，因此保守性更小。该方法随后扩展到更一般的两种情况，即考虑模式相关时变时滞和参数不确定性。最后，通过三个数值实例验证了所提出方法的性能和有效性。
