时间标度上时滞脉冲复值神经网络的全局稳定性  

Global Stability of Impulsive Complex-Valued Neural Networks With Time Delayon Time Scales

作　　者：闫欢[1] 宋乾坤[2] 赵振江[3] 

机构地区：[1]重庆交通大学信息科学与工程学院,重庆400074 [2]重庆交通大学数学系,重庆400074 [3]湖州师范学院数学系,浙江湖州313000

出　　处：《应用数学和力学》2015年第11期1191-1203,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(61273021;61473332);重庆市研究生科研创新项目(CYS14163)~~

摘　　要：研究了时间标度上具有时滞和脉冲影响的复值神经网络的全局稳定性问题.利用时间标度上的微积分理论,将连续时间型复值神经网络和离散时间型复值神经网络统一在同一个框架下进行研究.在不要求激励函数有界的条件下,运用同胚映射原理,建立了确保时滞复值神经网络平衡点存在性和唯一性的判定条件.通过构造合适的Lyapunov-Krasovskii泛函,并使用自由权矩阵方法和矩阵不等式技巧,获得了时间标度上具有时滞和脉冲影响的复值神经网络平衡点全局稳定性的充分条件.给出的判据是由复值线性矩阵表示的,易于MATLAB软件的YALMIP Toolbox实现.数值仿真实例验证了获得结果的有效性.The global stability of impulsive complex-valued neural networks with time delay on time scales was investigated. Based on the time scale calculus theory, both the continuous-time and discrete-time neural networks were described under the same framework. For the consid- ered complex-valued neural networks, the activation functions need not be bounded. According to the homeomorphism mapping principle in the complex domain, a sufficient condition for the existence and uniqueness of the equilibrium point of the addressed complex-valued neural networks was proposed in complex-valued linear matrix inequality （LMI）. Through the construction of appropriate Lyapunov-Krasovskii functionals, and with the free weighting matrix method and matrix inequality technique, a delay-dependent criterion for checking the global stability of the complex-valued neural .networks was established in the complex-valued LMIs. Finally, a simulation example shows the effectiveness of the obtained results.

关 键 词：复值神经网络 时间标度 时滞 脉冲 复值线性矩阵不等式 全局稳定性 

分 类 号：O175.13[理学—数学]