Consistency Analysis of some Closed-Loop Subspace Identification Methods

We study statistical consistency of two recently proposed subspace identification algorithms for closed-loop systems. These algorithms may be seen as implementations of an abstract state-space construction procedure described by the authors in previous work on stochastic realization of closed-loop systems.A detailed error analysis is undertaken which shows that both algorithms are biased due to an unavoidable mishandling of initial conditions which occurs in closed-loop identification. Instability of the open loop system may also be a cause of trouble.