Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, Heilongjiang Province, 150001, China.
Neural Netw. 2010 Apr;23(3):315-21. doi: 10.1016/j.neunet.2009.12.001. Epub 2009 Dec 3.
This paper investigates the problem of stability analysis for bidirectional associative memory (BAM) neural networks with Markovian jumping parameters. Some new delay-dependent stochastic stability criteria are derived based on a novel Lyapunov-Krasovskii functional (LKF) approach. These new criteria based on the delay partitioning idea prove to be less conservative, since the conservatism could be notably reduced by thinning the delay partitioning. It is shown that the addressed stochastic BAM neural networks with Markovian jumping parameters are stochastically stable if three linear matrix inequalities (LMIs) are feasible. The feasibility of the LMIs can be readily checked by the Matlab LMI toolbox. A numerical example is provided to show the effectiveness and advantage of the proposed technique.
本文研究了具有马尔可夫跳变参数的双向联想记忆（BAM）神经网络的稳定性分析问题。基于一种新的李雅普诺夫-克拉索夫斯基泛函（LKF）方法，得出了一些新的时滞相关随机稳定性准则。这些基于时滞分区思想的新准则证明具有较小的保守性，因为通过减少时滞分区可以显著降低保守性。结果表明，所研究的具有马尔可夫跳变参数的随机 BAM 神经网络是稳定的，如果三个线性矩阵不等式（LMI）是可行的。LMI 的可行性可以通过 Matlab LMI 工具箱方便地检查。给出了一个数值例子来说明所提出技术的有效性和优势。
