Retraction Note to: Using Inner-Outer Factorization to Solve the Spectral Factor of Discrete-Time Descriptor Systems

In this paper, we use the state-space realization of discrete-time descriptor system to solve the inner-outer and spectral factorization problems. The algorithm is based on finding two orthogonal matrices to decompose the pole separated realization of transfer function matrix, to get a stabilizing solution by sloving a algebraic Riccati equation which order usually smaller than the McMillan degree of the transfer function. We give a theorem to discuss the relation of inner-outer and spectral factorization and get the inner-outer factor of the system. Thus, the inner-outer factor is the spectral factor of the system. Finally, a simple numerical example is also illustrated.