Delay structure conditions for identifiability of closed loop systems

-When identifying a linear system operating under a linear feedback law, specific restrictions have to be imposed on the presence of delays in the plant and/or the controller in order to obtain identifiability. In this paper the delay structure conditions are investigated under which a least squares direct type prediction error identification method is able to consistently estimate the open loop plant. It is shown that the commonly required condition of strictly properness of the loop transfer function can be relaxed to a condition that relates to the absence of algebraic loops in the closed loop plant models.