Singular value decomposition for a class of linear time-varying systems with application to switched linear systems

The present paper considers singular value decomposition (SVD) for a class of linear time-varying systems. The class considered herein describes time-driven switched linear systems. 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. The SVD is then applied to switched linear systems to improve the transient response. A numerical example is provided to demonstrate the proposed method.