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This paper deals with singular value decomposition (SVD) for a class of linear time-varying systems. The class considered here describes switched linear systems with periodic switching. Based on an appropriate input-output description, the calculation method of singular values and singular vectors is derived. The SVD enables us to characterize the dominant input-output signals using singular vectors, which form orthogonal systems in input and output spaces. Then SVD is applied to switched linear systems to improve the transient response. A numerical example is provided to demonstrate the proposed method.