中立型随机时滞系统的渐近稳定性

通过It^o公式与半鞅收敛定理建立了中立型随机时滞系统的拉萨尔不变原理,确定系统解的极限位置的判定条件,并应用此原理给出中立型随机时滞系统的渐近稳定性的充分条件.同时也说明了本方法的结果包含了经典的随机系统稳定性结果为其特殊情况.需要指出的是,本方法所建立的稳定性结果无须LV负定,充分利用了随机扰动项的作用.最后,用实例验证了该结果.

Asymptotic stability of neutral stochastic differential delay systems

The LaSalle-type theorem for the neutral stochastic differential delay equations was established by using It formula and semimartingale convergence theorem.According to the theorem,some sufficient criteria for the stochastically asymptotic stability of the neutral stochastic differential equations with delay were obtained.It was shown that the well-known classical theorem on stochastic asymptotic stability was a unique case among our more general results.Compared with the classical stochastic stability results,the stability criteria in this paper made the best use of the effects of stochastic disturbed term in stochastic systems and canceled the requirements of the negative definite of L_V.Finally,an example was given for the illustration.