This technical note presents a hybrid control scheme for the output-feedback control of switched linear systems with average dwell time. The proposed hybrid controller consists of a standard switching output-feedback control law and a supervisor enforcing a reset rule for the switching controller states at each switching instant. This hybrid control scheme provides an efficient and systematic way for designing average dwell time switched linear control systems in the sense that the boundary condition can be incorporated into the synthesis problem in a convex formulation. Specifically, both full-order and reduced-order controllers with guaranteed stability and optimal weighted H-infinity performance will be solved by linear matrix inequality (LMI) optimizations. Simulation studies are included to illustrate the effectiveness of the proposed approach.