Robust L2-L∞ filtering of stochastic repetitive processes

In this paper, we investigate the problem of L₂-L_infin filtering for a class of stochastic linear continuous repetitive processes. Attention is focused on the design of full-order filter that guarantees the filtering error repetitive processes to be mean-square asymptotically stable and to have a prespecified L₂-L_infin performance gamma 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.