This article deals with switched state-feedback H-2 control design of continuous time-varying polytopic systems. More specifically, the main goal is to determine, simultaneously, a set of state-feedback gains and a switching rule to orchestrate them, rendering the closed-loop system globally asymptotically stable for all time-varying uncertain parameter under consideration and assuring a guaranteed H-2 cost. A contribution of the present switched control technique compared to the gain scheduling, widely used in the literature, is that the online measurement of the uncertain parameter is not required and no assumption on its time derivative is imposed. The conditions are based on modified Lyapunov-Metzler inequalities and can be solved by line search coupled with LMIs. An academic example illustrates the theoretical results and compares the present technique with other techniques from literature.