SUMMARYThis paper proposes an identification algorithm for time-varying systems. We apply subspace method for estimation, since it is known to be useful when the input-output (I/O) data are observed by multi-input multi-output (MIMO) systems. Among many proposed techniques of subspace methods, we use MOESP (MIMO Output-Error State Space model identification) in this paper, which assures arithmetic stability by RQ factorization and singular value decomposition (SVD). Generally, subspace methods can be applied after I/O data collection, so that we introduce updated steps of matrices for PI-MOESP, which uses past inputs for instrumental variables. We propose a recursive update algorithm of PI-MOESP, including estimation step of the system order, and consider some parameters inherent to the algorithm, namely, initial number of data, estimation step of the order, and forgetting factor. A numerical example shows the usefulness of the proposed method.
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