This paper presents a new switching control approach for robust output feedback control of a class of discrete-time linear systems subject to polytopic time-varying uncertainties. The proposed robust switching controller, which stabilizes the closed-loop system with a pre-specified H∞ performance level, consists of a family of dynamic output feedback controllers (of an arbitrary state order) and a switching law (the relaxed min-switching strategy). Both stability analysis and control synthesis conditions are derived using a piecewise quadratic Lyapunov function. The switching law combined with the controller gain matrices are jointly synthesized by solving a convex linear matrix inequality (LMI) based optimization problem. An academic example has been used to demonstrate the effectiveness and advantages of the proposed approach.