随机时滞系统的渐近稳定性

应用多个李雅普诺夫函数讨论了随机时滞系统解的渐近行为，通过伊藤公式与半鞅收敛定理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随机时滞系统渐近稳定性的有效判据，使实际应用中构造李雅普诺夫函数更为方便．同时也说明了本研究的结果包含了经典的随机系统稳定性，且经典的结果为本研究结果的特殊情况．本研究所得到的结果无须Lv负定，充分利用了随机扰动项的作用，并且从理论上解释了一个不稳定的系统有时加入适当随机扰动后反而稳定的原因．

Asymptotic stabilities of stochastic delay systems

This paper discussed asymptotic characteristic of the solution of the stochastic delay systems and established sufficient condition via multiple Lyapunov functions for locating the limit set of the solution by using Ito^ formula and semi-martingale convergence theorem. Moreover, many effective criteria of stochastic asymptotic stability were obtained , which enabled us construction of the Lyapunov functions much more easily in application. It was shown that the well-known classical theorem about stochastic asymptotic stability is a special case of the given more general results. The operator Lv in this paper is not required to be negative definite and made best use of the effect of the stochastic perturbation. Furthermore, it showed theoretically that an unstable system, which is disturbed by stochastic noise at some time, will become stable.