This paper deals with robust stabilization of nonlinear systems represented by uncertain and disturbed switched Takagi-Sugeno fuzzy systems. First, stabilization of uncertain switched fuzzy systems is considered without external disturbances. A stabilization criterion is proposed as sufficient Linear Matrix Inequality (LMI) conditions. These ones allow designing a switched parallel distributed compensation fuzzy control law based on a candidate switched Lyapunov function. Then, an extension to systems subject to external disturbances is provided based on a H-infinity criterion. To illustrate the effectiveness of the proposed stabilization criterion and controller design approaches, a designed numerical example is studied and some simulations are provided.