Abstract: The non-fragile robust H∞ control problem is investigated for a class of uncertain switched nonlinear systems with additive gain variations. A design scheme is then given to the non-fragile feedback controllers with their switching law proposed. With the multiple Lyapunov functions used, the switching between subsystems makes the switched nonlinear systems asymptotically stable with H∞-norm bound for all allowable uncertainties. Thus, the sufficient condition solvable to the problem doesn't depend on the Hamilton-Jacobi inequalities. This method is suitable for the case where none of subsystems is asymptotically stable. Then, as a special application, a feedback strategy is proposed to solve the standard non-fragile robust H∞ control problem for non-switched nonlinear systems when no single continuous controller is effective. An example is given to verify the effectiveness of the proposed method.