具有可变时滞的中立型随机系统的渐近性质

Asymptotic properties for neutral stochastic systems with time-varying delay

本文研究了一类具有可变时滞的中立型随机系统解的渐近性质.利用Lyapunov函数It、^o公式和上鞅收敛定理,得到了该系统解的一些几乎必然渐近稳定性与p阶均值渐近稳定性、几乎必然多项式渐近稳定性与p阶均值多项式渐近稳定性及几乎必然指数稳定性与p阶均值指数稳定性的充分判据.与经典的随机稳定性结论相比,本文所建立的判据充分利用了随机扰动项的作用,无须LV(扩散算子)的负定.

The asymptotic properties of a class of neutral stochastic systems are discussed.By using Lyapunov function,Itǒ formula and super-martingales convergence theorem, sufficient criteria on its almost sure asymptotic properties, p-order mean asymptotic properties, almost sure polynomial asymptotic stability, p-order mean polynomial asymptotic stability, almost sure exponential stability and p-order mean exponential stability are obtained. Compared with the classical stochastic stability results, the proposed stability criteria make the best use of the effects of stochastic disturbed term in stochastic systems and cancel the requirement of the negative definite of LV（diffusion operator）.