实践中由于成本等因素的约束，考虑系统的有限时间稳定性往往会比考虑传统的稳定性更具实用性和经济性 . 文中讨论了一类二次型离散系统的有限时间稳定与镇定，通过采用线性矩阵不等式将反馈控制增益矩阵的设计转化为线性矩阵不等式组的求解问题，给出了状态反馈控制下使闭环系统有限时间稳定的充分条件和反馈控制增益矩阵的设计方法 . 该方法也适用于系统存在外源干扰的情形，可以使具有干扰的系统实现有限时间有界 . 最后，用数值例子做仿真验证，仿真结果和理论分析结果一致，表明文中方法是可行的 

In practice ， finite-time stability of systems is more practical and economical than the traditional stability due to costs and other constraints. This paper studies the finite-time stability and stabilization for a class of quadratic discrete-time systems. By means of linear matrix inequality ， the design of feedback control gain matrix is converted into the solutions for linear matrix inequalities. Moreover ， sufficient conditions for the finite-time stability of closed-loop systems with state feedback are determined ， and a method to design the feedback control gain matrix is proposed to achieve the finite-time stability of systems. This method is also suitable to deal with the finite-time boundedness of systems with exogenous disturbance. Finally ， numerical examples are used for validation. The consistency of simulation and theoretical analysis results proves the feasibility of the proposed method.