In this paper the synthesis of multiple controllers for a class of time-varying nonlinear systems is considered. The proposed hybrid control scheme is based on a fuzzy supervisor which manages the combination of controllers of two types: with sliding mode control (SMC) and H_inf control. A convex formulation of the two controllers leads to a structure which benefits from the advantages of both controllers to (i) ensure a good tracking performance in both the transient state (SMC) and the steady state (H_inf), (ii) provide a fast dynamic response to enlarge the stability limits of the system, and (iii) efficiently reduce the chattering phenomena induced by the SMC. The stability analysis uses the Lyapunov technique, inspired from switching system theory, to prove that the system with the proposed controller remains globally stable despite the configuration changing. Some simulation results and conclusions end the paper.