一类脉冲随机系统的有限时间有界性分析与H∞控制
Finite-time boundedness analysis and H-infinity control for a class of impulsive stochastic systems

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。
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 Hinfinity 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.