Inner-outer factorization of discrete-time transfer function matrices

The inner-outer factorization of the transfer function matrix of a linear time-invariant system has been an important algebraic problem in a variety of areas in electrical engineering, including systems and control analysis and design. This paper gives an explicit state space-based algorithm for the inner-outer factorization of the transfer function matrix of a general discrete-time linear system. More specifically, the algorithm applies to any discrete-time linear system whose transfer function is proper and stable.