Abstract
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.
The earlier version of this paper was presented at the International Symposium on Mathematical Theory of Networks and Systems, Kyoto, July 2006.
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Katayama, T. (2007). Role of LQ Decomposition in Subspace Identification Methods. In: Chiuso, A., Pinzoni, S., Ferrante, A. (eds) Modeling, Estimation and Control. Lecture Notes in Control and Information Sciences, vol 364. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73570-0_17
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DOI: https://doi.org/10.1007/978-3-540-73570-0_17
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