基于凸组合的一类时变时滞静态神经网络系统全局稳定性分析  

Analysis on the Stability of the Static Neural Networks with Time-varying Delays Based on the Convex Combination

作　　者：毛凯 杨树杰 刘丹 MAO Kai;YANG Shujie;LIU Dan(Teaching and Research Section of Mathematics,College of Basic Science for Aviation,Naval Aviation University,Shandong Yantai 264001,China)

机构地区：[1]海军航空大学航空基础学院数学教研室

出　　处：《河南大学学报（自然科学版）》2019年第6期731-738,750,共9页Journal of Henan University:Natural Science

基　　金：国家自然科学基金项目(11802338)

摘　　要：研究了一类具有时变时滞的静态神经网络系统的全局渐近稳定性问题,考虑了更多时滞状态变量的信息,构造新的增广Lyapunov-Krasovskii泛函,利用时滞分割技术并结合使用自由权矩阵、Jensen积分不等式,基于凸组合方法获得具有更低保守性的系统时滞相依全局渐近稳定性判定条件,改善了相关文献结果,并以数值实例表明本文结果的有效性.The globally asymptotical stability for static neural networks with time-varying delay is studied in this paper. By taking more delayed-state variables into account, a newly augmented Lyapunov-Krasovskii functional is constructed. By using of the delay fractitioning approach together with the free weighing matrix method and Jensen integral inequality, a delay-dependent global asymptotical stability criterion is obtained based on the convex combination method, which is less conservative than some existing ones. Example is provided to show the effectiveness and reduced conservatism of the proposed results.

关 键 词：静态神经网络 LYAPUNOV-KRASOVSKII泛函 时滞分割 自由权矩阵 凸组合 线性矩阵不等式 

分 类 号：O175.13[理学—数学]