Design of switching 𝐻2/𝐻∞ output-feedback controller for discrete-time LTI systems with state-multiplicative noise is considered. The closed loop system achieves a minimum bound on the stochastic 𝐻2 performance level, while satisfying the 𝐻∞ performance. The proposed controller is based on a fuzzy supervisor which manages the combination of two separate 𝐻2 and 𝐻∞ controllers. A convex formulation of the two controllers leads to a structure which benefits from the advantages of both controllers to ensure a good performance in both the transient phase (𝐻2 controller) and the steady phase (𝐻∞ controller). The stability analysis uses the Lyapunov technique, inspired from switching system theory, to prove that the closed loop system with the proposed controller structure remains globally stable despite the configuration changing.