中文摘要：

针对线性离散周期系统的状态反馈控制问题，利用提升法将线性离散周期系统转化为时不变系统并提出期望极点指标，同时要求周期系统满足H2范数指标，采用数值递推算法对线性周期系统进行上述指标的满意控制设计，并运用满意控制思想将上述控制问题转化为线性矩阵不等式（LMI）的线性凸优化问题，从而运用LMI技术求解、设计可行的满意控制。数值仿真验证了相关结论。

英文摘要：

Problems of state feedback for linear discrete-time periodic systems are studied. Firstly regional pole index for the periodic system is set up through lifting technique and the other index of H2 norm for the periodic systems is also required simultaneously. And then satisfactory control for the linear periodic systems with pole and He norm requirements is designed by using of recursion algorithm. And this problem of satisfactory control for the periodic systems can be converted into a linear convex optimization problem based on satisfactory control idea by Linear Matrix Inequalities （LMI）. Finally a feasible satisfactory control sketch is achieved and checked bY a simulation example.