Robust L₂-L_∞ Filtering of Uncertain Stochastic Linear Repetitive Processes

The problem of robust L₂-L_∞filtering for a class of uncertain stochastic linear repetitive processes is investigated. A full-order filter is designed which guarantee mean-square asymptotically stable of uncertain stochastic linear repetitive processes.The sufficient conditions for the existence of L₂-L_∞full-order filter are proposed,and the corresponding filter design is cast into a convex optimization problem.The designed full-order filter can ensure L₂-L_∞performance is smaller than given γ for the repetitive processes with respect to all energy-bounded external disturbance signals.A numerical example illustrates the effectiveness of the proposed design scheme.