Subspace Identification of Closed Loop Systems by Stochastic Realization

We develop a closed loop subspace identification method based on stochastic realization theory. Using the preliminary orthogonal decomposition of (Picci and Katayama, 1996b) we show that, under the assumption that the exogenous input is feedback-free and persistently exciting (PE), the identification of closed loop systems is divided into two subproblems: the deterministic identification of the plant and controller, and the stochastic identification of the noise filter. Subspace methods for identifying the deterministic and stochastic parts are derived by adapting the standard subspace methods to the deterministic and stochastic components. In both cases, a model reduction procedure should be applied in order to extract controllable and observable parts from non-minimal realizations. Some numerical results are included to show the applicability of the present technique.