Non-linear H-infinity-controller synthesis is developed for time-periodic systems via measurement feedback. Interest is focused on a periodic controller design. Both global and local solutions of the problem are derived. The global solution is based on a suitable solution to appropriate Hamilton-Jacobi-Isaacs inequalities, whereas the local solution is derived by means of a certain perturbation of the differential Riccati equations appearing in solving the linear H-infinity-control problem for the linearized system. Theoretical results are supported by simulation of H-infinity-tracking control of a robot manipulator.