针对线性周期多采样率系统的满意滤波问题,根据满意估计思想,将结构不确定周期系统满足滤波系统稳定与H∞指标的满意估计问题转化为Riccati矩阵不等式求解问题,无须采用通常的提升手段而直接运用数值法与内点法进行周期系统多指标设计.利用线性矩阵不等式技术(LMI)提出了一种基于LMI的满意滤波器设计方法.仿真例子验证了相关的结论. According to the idea of ​​satisfactory estimation, a satisfactory solution to the problem of satisfying the linear periodic multi-sampling rate system is proposed. The problem of satisfying the stability of the uncertain periodic system and the H∞ index is considered as the Riccati matrix inequality problem. The numerical method and the interior point method are used to carry out the multi-index periodic system design. A LMI-based method for designing a satisfactory filter is proposed by using linear matrix inequalities (LMIs). The simulation examples verify the relevant conclusions.