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.