In this article, synthesis of switching H2/H∞ controller is considered which results in the minimum bounds on H2 and H∞ performance levels. The fuzzy supervisor manages the controllers and results in the structure that benefits from the advantages of them. The suggested structure guarantees the desired performance in transient and steady state modes and is solvable through linear matrix inequalities approach. By means of multi- Lyapunov functions the stability has been approved and despite the structure changing, the system remains global stable. The suggested intelligent synthesis is less complicated in comparison with common approaches based on common Lyapunov function due to using separate controllers and eliminating the constraint of common Lyapunov function. The results of those methods of H2/H∞ control can simply be calculated from the suggested approach.