Role of LQ Decomposition in Subspace Identification Methods.

We revisit the deterministic subspace identification methods for discrete-time LTI systems, and show that each column vector of the L-matrix of the LQ decomposition in MOESP and N4SID methods is a pair of input-output vectors formed by linear combinations of given input-output data. Thus, under the assumption that the input is persistently exciting (PE) of sufficient order, we can easily compute zero-input and zero-state responses by appropriately dividing given input-output data into past and future in the LQ decomposition. This reveals the role of the LQ decomposition in subspace identification methods. Also, a related issue in stochastic realization is briefly discussed in Appendix. [ABSTRACT FROM AUTHOR]