Direct subspace model identification of LTI systems operating in closed-loop

In this paper, a subspace identification method of estimating the input-output relation of a linear system operating in closed-loop is presented. The proposed method is a straightforward consequence of the integration of the two-stage method with PI-MOESP type subspace identification method. It is shown that such integration brings the omission of the first stage identification, i.e., the omission of the identification of the sensitivity function of closed-loop and subsequent reconstruction of the fictitious input sequence. Therefore, the proposed method is able to estimate the input-output relation of a linear system in closed-loop directly from sampled sequences of observed signals.