Closed loop realization algorithms via a joint-input-output approach

This paper studies a closed loop realization problem, revisiting an identifiability condition of linear systems under feedback. It is shown that two joint-input-output algorithms can be derived from the analysis of the closed loop matrix and its inverse based on spectral factorization and stochastic realization theories. The algorithm based on the inverse of the closed loop matrix is given by means of left coprime factor representations of the plant and controller.