Abstract: The paper investigates the problem of L₂-L_∞ filtering for a class of stochastic linear repetitive processes.Attention is focused on the design of full-order filter guaranteeing mean-square asymptotical stable of stochastic linear repetitive processes and a prespecified L₂-L_∞ performance γ for the filtering error processes with respect to all energy-bounded input signals.Sufficient conditions are proposed in terms of linear matrix inequality，and the corresponding filter design is cast into a convex optimization problem.A numerical example illustrates the effectiveness of the proposed design scheme.

摘要： 针对随机线性重复过程，研究了其鲁棒L₂-L_∞滤波问题。基于线性矩阵不等式技术推导了该随机线性重复过程均方渐近稳定以及鲁棒L₂-L_∞全阶滤波器存在的充分条件，并将滤波器的设计转化为一个凸优化的求解问题。所设计的滤波器能够保证相对于所有能量有界的外界扰动信号，重复过程的L₂-L_∞性能指标小于一定值γ。仿真实例证实了该设计方法的有效性。