不动点技巧在反应扩散模糊随机周期时滞系统稳定性分析中的应用  

Application of the Fixed Point Approach to Stochastic Stability Analysis for the Periodic Reaction-Diffusion T-S Fuzzy System with Time Delays

作　　者：李兴贵[1] 黄家琳 LI Xing-gui;HUANG Jia-lin(Department of Mathematics,Chengdu Normal University,Chengdu 611130,China;Department of Basic Courses,Sichuan Sanhe Vocational College,Luzhou Sichuan 646200,China)

机构地区：[1]成都师范学院数学系,成都611130 [2]四川三河职业学院基础部,四川泸州646200

出　　处：《西南大学学报（自然科学版）》2019年第6期64-72,共9页Journal of Southwest University(Natural Science Edition)

基　　金：国家973项目(2010CB732501);四川省科技厅基础研究计划项目(2012JYZ010)

摘　　要：利用不动点定理、变分方法、线性矩阵不等式技巧、李雅普诺夫方法和Banach压缩映射原理,给出了线性矩阵不等式条件的反应扩散马尔科夫跳跃周期模糊时滞系统的随机稳定性判据,并通过建立在乘积空间上的压缩映射克服了反应扩散模型带来的数学上的困难.最后,利用数值实例证实了所述方法的有效性.By applying the fixed-point theorem,the variational method,the linear matrix inequality (LMI) technique and the Lyapunov functional and Banach contraction mapping principle,the authors derive a new LMI-based global exponential stability criterion for the Markovian jumping reaction-diffusion T-S fuzzy BAM neural networks. It is worth mentioning that the difficulties caused by the reaction-diffusion BAM neural networks can be overcome by defining a contraction mapping on a product space. A numerical example is given to show the validity of the proposed method.

关 键 词：反应扩散 双向联想记忆神经网络 周期解 马尔科夫跳跃 

分 类 号：O193[理学—数学]