摘要
研究了一类具有可变时滞的中立型非线性随机系统解的渐近性质,利用李亚普诺夫函数和半鞅收敛定理,得到了该系统解的三个渐近性质不等式;通过伊藤公式与半鞅收敛定理及不等式技巧建立了确定这种系统解的极限位置的充分条件,并且从这些条件得到了中立型非线性时滞随机系统解的渐近稳定性、多项式渐近稳定性及指数稳定性有效判据,其结果涵盖并推广了毛学荣关于中立型非线性随机系统解的渐近性质方面的部分结论.
The asymptotic properties of one type of nonlinear neutral stochastic systems were discussed. By Lyapunov function and supermartingales convergence-theorem, three results on inequalities with its asymptotic properties are given. Sufficient condition for locating the limit set of the solution by using Ito formula and semi-martingale convergence theorem and inequality technology were established, and asymptotic characteristic, such as asymptotic stabilities, polynomial stabilities and exponential stabilities, of the solution of the nonlinear neutral stochastic systems with delays are obtained. All the results imply and generalize the partial conclusions on asymptotic properties of nonlinear neutral stochastic systems Mao discussed in existing references.
出处
《华中科技大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2006年第10期61-63,92,共4页
Journal of Huazhong University of Science and Technology(Natural Science Edition)
基金
国家自然科学基金资助项目(60574025
60474011)
湖北省自然科学基金资助项目(2004ABA055)
关键词
中立型非线性随机系统
渐近稳定性
李亚普诺夫函数
上鞅收敛定理
伊藤公式
nonlinear neutral stochastic systems
asymptotic stability
Lyapunov function
super-mar tingales convergence theorem
Ito＇s formula
