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The stabilization of a class of single input switched nonlinear systems is investigated in the paper. The systems concerned are of switched upper-triangular structure. The stabilization of the switched system under some switching law is investigated. Sufficient conditions are given under which the globally asymptotically stabilization problem is solvable. We exploit the structural characteristics of the switched nonlinear systems to construct the Lyapunov functions. The switching law and a nonlinear switched state feedback controller are explicitly designed. The relevant result for the linear switched system with the same structure is particularized.