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Finite-time stability of a class of switched systems is discussed. First, the definition of set finite-time stability of switched systems is proposed, and sufficient conditions under witch switched systems is finite-time stable are also given. Finite-time stability results are proved by using common Lyapunov-like function and multiple Lyapunov-like functions respectively. Moreover, based on the proposed method, output finite-time stability of a class of switched linear systems is discussed. An example is employed to verify the proposed method.