中文摘要：

本文利用Lyapunov方法研究了线性离散广义系统的有限时间控制问题．针对该系统的开环情形，给出了其有限时间稳定的充分条件．在此基础上，设计状态反馈控制器，给出了其闭环系统是有限时间有界的充分条件．特别地，针对具有外源干扰线性离散广义系统，我们也给出了控制器设计方法和保证其闭环系统有限时间有界的充分条件．最后通过数值算例验证了该方法的有效性．

英文摘要：

In this paper, the finite-time control problem is considered for discrete linear sin- gular systems by virtue of Lyapunov＇s method. The sufficient conditions for the finite-time stability of the open-loop discrete linear singular systems are given. Based on the conditions, a state controller is designed and the sufficient conditions for the finite-time boundedness of the closed-loop system composed by the state controller and the discrete linear singular system are presented. In particular, we consider a discrete linear singular system subject to an ex- ogenous output, and provide a designing method of controller and the sufficient conditions for the finite-time boundedness of the closed-loop system composed by the controller and discrete linear singular system subject to an exogenous output. Finally, a numerical example illustrates the validity of the proposed approach.