随机可变时滞系统的渐近稳定性

Asymptotic stability of stochastic systems with variable delay

讨论了一类随机可变时滞系统解的渐近稳定性。应用It 公式、半鞅收敛定理与多个Lyapunov函数建立了这类随机可变时滞系统渐近稳定性的有效判据,使实际应用中构造Lyapunov函数更为方便。同时也说明了结果包含经典的随机系统稳定性结果为其特殊情况。与经典的随机稳定性理论相比,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,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。最后。

Asymptotic stability of the solution to a class of stochastic systems with variable delay is discussed. And effective criteria on stochastic asymptotic stability for the systems are established by using Ito formula, semi-martingale convergence theorem and some Lyapunov functions, which enable us to construct the Lyapunov functions much more easily in application. It is shown that the well-known classical theorem on stochastic asymptotic stability is a special case of more general results obtained. Compared with the classical stochastic stability results, the stability criteria established make the best use of the effects of stochastic disturbed term in stochastic systems and cancel the requirement of the negative definite of LV. Furthermore, it is shown theoretically that an unstable system, which is disturbed by stochastic noise, will become stable sometimes. In the end, an example is given for illustration.