一类脉冲随机系统的有限时间有界性分析与H∞控制

摘要

This paper is concerned with the problem of the finite-time boundedness and H-infinity control for a class of linear impulsive stochastic systems.First,employing Lyapunov functions and the average impulsive interval technique,a theorem on the finite-time boundedness in the sense of mean square is established.Then,based on the theory of H-infinity control,a criterion guaranteeing both the finite-time boundedness and a certain H-infinity performance index is derived.Also,for the finite-time H-infinity control problem,some sufficient conditions for the existence of a state feedback controller are proposed.Finally,a numerical example is given to verify the effectiveness of the theoretical results.%本文研究一类线性脉冲随机系统的有限时间有界性及H∞控制问题.首先,利用Lyapunov函数和平均脉冲区间条件,建立了系统有限时间均方有界定理;其次,基于H∞控制理论,获得了保证系统有限时间有界且满足一定的H∞性能指标的判据;再次,针对有限时间H∞控制问题,给出了状态反馈控制器存在的充分条件.最后,用一个数值例子表明了理论结果的有效性.