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This paper investigates the problems of L2 stability and H∞ control problem of a class switched homogeneous nonlinear system via the semi-tensor product (STP) of matrices method. First, a homogeneous Lyapunov-like function in the form of STP is constructed. Based on this, the system in question is limited on to the unit sphere to be investigated, a switching law is designed to make sure that the normal system that is globally asymptotically stable is globally L2 stable either. By the former Lyapunov-like function and the designed switching law, the H∞ control problem of the considered system is reduced into a Riccati-like one via the STP of matrices method, thus a control law similar to that of linear system is designed.