基于LMI的混合时滞随机神经网络指数稳定性

LMI-Based Approach for Exponential Stability of Stochastic Neural Networks with Hybrid Time-Delays

为研究具有混合时滞的随机反馈神经网络的平衡解的稳定性问题,基于Lyapunov稳定性理论及Ito随机微分公式计算了随机神经网络得到在均方意义下的全局指数稳定性。利用网络模型中混合时滞的形式特点构造了新型的Lyapunov-Krasovskii泛函,并借助矩阵不等式分析技巧建立了新型采用线性矩阵不等式形式的判别条件,较已有采用矩阵范数形式的判别条件放宽了要求。线性矩阵不等式可以利用Matlab中提供的线性矩阵不等式进行计算验证,使得所得判别条件更加实用。最后给出了数值证明判别条件的有效性。

This paper deals with the problem of stability for the equilibrium solution of a class of stochastic neural networks with hybrid time - delays.Based on Lyapunov stability theory and It？ formula,mean square exponential stability for the solutions of stochastic neural network is discussed.According to the hybrid delays in neural network, constructing new Lyapunov-Krasovskii functional,by means of method of matrix inequality analysis,new criteria is derived in terms of linear matrix inequalities.The conservatism of new conditions is less than that given by matrix norm.Linear matrix inequality can be readily checked by using Matlab LMI Toolbox,such that the criteria is more practical.A numerical example is provided to demonstrate the applicability and effectiveness of the proposed criteria.