不确定随机时滞反应扩散广义细胞神经网络的有限时间鲁棒稳定性  

Finite-Time Robust Stochastic Stability of Uncertain Stochastic Delayed Reaction-Diffusion Generalized Cellular Neural Networks

作　　者：罗兰[1] 刘正龙[1] 

机构地区：[1]川北医学院计算机与数学教研室,四川南充637000

出　　处：《四川师范大学学报（自然科学版）》2014年第2期208-215,共8页Journal of Sichuan Normal University（Natural Science）

基　　金：四川省教育厅自然科学青年基金(12ZB040)资助项目

摘　　要：细胞神经网络已成为应用数学领域研究的热点之一.时滞、反应扩散、不确定项的引入对于广义细胞神经网络的研究具有实际意义.在实际中,需要知道系统在某个固定的时间间隔的动态行为,即系统的有限时间稳定性.在不确定项范数有界的条件下,通过构造Lyapunov泛函,运用Ito公式和稳定性理论,给出了系统的有限时间鲁棒稳定性的充分条件,这些条件既依赖于时滞又依赖于反应扩散项.最后的数值举例表明了结论的有效性.One of research focuses in applied Mathematics is cellular neural networks. Delay, reaction diffusion, and the uncer- tainties introduced in generalized cellular neural network have real significance. In practice, we need to know the system＇ s dynamic be- havior in fixed time interval, namely the finite-time stability of the system. In the condition of the norm-bounded uncertainties, by con- structing the Lyapunov function, applying the Ito＇ s formula and the theory of stability, the sufficient conditions ensuring the networks to be finite-time robustly stochastically stable are established. These conditions not only depend on the delays but also depend on the reac- tion-diffusion. Finally, a numerical example demonstrates the feasibility of the present conclusions.

关 键 词：广义细胞神经网络 有限时间鲁棒稳定性 时滞 反应扩散 随机扰动 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]