Abstract: The satisfactory filter problem is studied for linear multi-rate periodic systems with parameter uncertainty. The problem under consideration is to design a satisfactory filter such that the resulting filtering system is asymptotically stable and meets desired H-infinity rejection level for all admissible parameter uncertainty. Based on the satisfactory estimation idea, the problem is firstly converted into a problem of solving Riccati matrix inequalities (RMI). Then the latter is cast into a feasibility problem of a system of linear matrix inequalities (LMI) via matrix transform and LMI technique. A design method of satisfactory filter meeting desired multiple objectives is then provided which is effective by using Matlab-LMI computational software. Finally, a simulating example confirms the results obtained.