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针对随机控制系统数值解的均方指数输入状态稳定性

DOI: 10.3724/SP.J.1004.2013.01360, PP. 1360-1365

Keywords: 均方指数输入状态稳定性,随机控制系统,随机θ-方法,强收敛性

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Abstract:

?分析了随机控制系统数值解的均方指数输入状态稳定性.首先,针对随机控制系统,随机θ-方法满足有限时间强收敛条件.然后,我们证实,在有限时间强收敛条件下,随机控制系统是均方指数输入状态稳定的当且仅当随机θ-方法(充分小步长)是均方指数输入状态稳定的.另外,对一类满足单边Lipschitz条件的随机控制系统,有两类隐式欧拉方法(对任意步长)能够继承原系统的均方指数输入状态稳定性.最后,一些数值实例证实了本文所获结论的正确性.

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