Abstract
In this paper, recursive algorithms of subspace state‐space system identification (4SID) for multiple‐input, multiple‐output (MIMO), finite dimensional, linear time‐invariant (FDLTI) systems are proposed. These algorithms are derived based on the Matrix Inversion Lemma. The investigation of our algorithms clarifies that a series of 4SID is the extension of the classical least square method to identification for multivariable systems, and also that our algorithms are the direct extension of the recursive least square algorithm to such ones. For PO‐MOESP (the ordinary MOESP scheme with instrumental variables constructed from Past input and Output measurements), we show the mechanism of how the effect of the process and measurement noises is eliminated asymptotically by a projection related to the input and regressor matrices. “MOESP” is an abbreviation for “the MIMO output‐error state‐space model identification.”
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