Abstract: For an affine nonlinear system affected by internal and external disturbances, the discontinuous state feedback controllers are built by using switching technique and multiple Lyapunov function method with switching laws designed to ensure that for all allowable uncertainties the relevant closed-loop system possesses the prescribed L2-gain and is asymptotically stable. The main condition is given in form of a group of partial differential inequalities, among which the inequalities are more solvable than a general Hamilton-Jacobi inequality after introducing the sealer functions. This method transforms the H∞ control problem of general systems into that of a certain switched system and has strong robustness for the variation of system parameters.