This paper addresses the L2-gain analysis and control synthesis problem for a class of switched nonlinear systems affected by both time-varying uncertainties and external disturbances. Firstly, the L2-gain for the autonomous switched disturbed uncertain system is analyzed. Then, a switched state feedback control law is designed and the L2-gain is analyzed for the disturbed uncertain non-autonomous switched system. Sufficient conditions for these two cases are obtained using average dwell-time method incorporated with piecewise Lyapunov functions. The corresponding closed-loop disturbed uncertain switched system and the disturbed uncertain autonomous switched system are globally exponentially stable with a weighted L2-gain under the sufficient conditions. Both the piecewise Lyapunov functions and the average dwell-time based switching laws are constructed based on the structural characteristics of the uncertain switched system.