On Global Stability of Delayed BAM Stochastic Neural Networks with Markovian Switching
On Global Stability of Delayed BAM Stochastic Neural Networks with Markovian Switching
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DOI：
10.1007/s11063-009-9107-3
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发表时间：
2009-08
影响因子：
3.1
通讯作者：
Yurong Liu;Zidong Wang;Xiaohui Liu
中科院分区：
文献类型：
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作者：
Yurong Liu;Zidong Wang;Xiaohui Liu
研究了具有马尔可夫跳跃参数和混合时滞的随机双向联想记忆（BAM）神经网络的稳定性分析问题。研究了系统的全局渐近稳定性和全局指数稳定性。混合时延包括离散时延和分布式时延。在不假设突触连接权的对称性和激活函数的单调性和可微性的前提下，利用Lyapunov-Krasovskii稳定性理论和Itô微分规则分别建立了延迟BAM网络随机全局指数稳定和随机全局渐近稳定的充分条件。这些条件用一组线性矩阵不等式（lmi）的可行性来表示。因此，利用高效的Matlab LMI工具箱可以很容易地检查具有马尔可夫跳跃参数的延迟BAM的全局稳定性。通过一个简单的例子说明了所导出的基于lmi的稳定性条件的有效性。
In this paper, the stability analysis problem is investigated for stochastic bi-directional associative memory (BAM) neural networks with Markovian jumping parameters and mixed time delays. Both the global asymptotic stability and global exponential stability are dealt with. The mixed time delays consist ofboththe discrete delaysandthe distributed delays. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, we employ the Lyapunov–Krasovskii stability theory and the Itô differential rule to establish sufficient conditions for the delayed BAM networks to be stochastically globally exponentially stable and stochastically globally asymptotically stable, respectively. These conditions are expressed in terms of the feasibility to a set of linear matrix inequalities (LMIs). Therefore, the global stability of the delayed BAM with Markovian jumping parameters can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. A simple example is exploited to show the usefulness of the derived LMI-based stability conditions.