【作者】 龙述君；

【导师】 徐道义；

【作者基本信息】 四川大学 ， 应用数学， 2006， 硕士

【摘要】 本文研究了离散时滞神经网络、分布时滞神经网络、时滞脉冲神经网络与具有分布时滞的脉冲动力系统的解的渐近性态。在第一章中,利用比矩阵测度更一般化的非线性算子测度研究了离散时滞及分布时滞神经网络的指数稳定性,给出了判定指数稳定的充分条件。在第二章中,利用非负矩阵的谱半径、参数变易法及不等式分析技巧讨论了具有分布时滞的神经网络的全局指数稳定性。在第三章中,通过建立脉冲微分-积分不等式,研究了一类具有分布时滞的脉冲动力系统的全局指数稳定性,得到了其充分条件。在第四章中,通过应用Lyapunov ? Krasovskii型泛函,负定矩阵的性质以及柯西准则,研究了时滞脉冲神经网络的指数稳定性和渐近稳定性,得到了其依赖于时滞的充分条件,并以线性矩阵不等式的形式给出了这些条件。更多还原

【Abstract】 In this paper, we study the stability of neural networks with discrete delays ordistributed delays and delay systems with impulsive effect.In Chapter 1, we analyze the exponential stability of neural networks with discretedelays or distributed delays by nonlinear measure which is a generalization of matrixmeasure, and present the sufficient conditions for exponential stability.In Chapter 2, by using spectral radius of nonnegative matrix, variance of parame-ter and inequality technique, we study the exponential stability of neural networks withdistributed delays.In Chapter 3, by establishing impulsive differential-integro inequality, we analyzethe exponential stability of impulsive dynamical system with distributed delays, andgive the sufficient conditions for it.In Chapter 4, by using Lyapunov-Krasovskii type functional, the quality of nega-tive definite matrix and Cauchy criterion, we study the neural networks with impulsiveeffect and time varying delays, and obtain the sufficient conditions for global exponen-tial stability and global asymptotic stability of such model, in terms of linear matrixinequality(LMI), which depend on the delays.更多还原