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This paper is concerned with the Hinfin control problem for a class of non-minimum phase cascade switched nonlinear systems. The system under consideration is composed of two cascade-connected parts which are also switched systems. Sufficient conditions under which the Hinfin control problem is solvable under an arbitrary switching law are presented. The common Lyapunov function and the switched state feedback controller are constructed explicitly based on the structure characteristics of the switched system. The corresponding closed-loop switched system under consideration is globally asymptotically stable and achieves an prescribed L2-gain. The proposed method does not rely on the solutions of Hamilton-Jacobi equations.