An overview of subspace identification

Subspace identification methods (SIM) have enjoyed tremenous development in the last 15 years in both theory and practice. IMs offer an attractive alternative to input-output methods due o simple and general parametrization for MIMO systems (there s no linear input-output parametrization that is general enough or all linear MIMO systems, see (Katayama, 2005)). Most SIMs all into the unifying theorem proposed by van Overschee and de oor (1995), among which are canonical variate analysis (CVA) Larimore, 1990), N4SID (van Overschee & de Moor, 1994), ubspace splitting (Jansson & Wahlberg, 1996), and MOESP Verhaegen & Dewilde, 1992). Based on the unifying theorem, ll these algorithms can be interpreted as a singular value decomosition of a weighted matrix. The statistical properties such s consistency and efficiency have been investigated recently Bauer, 2003; Bauer & Ljung, 2002; Gustafsson, 2002; Jansson Wahlberg, 1998; Knudsen, 2001). The closed-loop identification is of special interest for a large umber of engineering applications. For safety reasons or quality estrictions, it is desirable that identification experiments are caried out under the closed-loop or partial closed-loop condition. s pointed out by many researchers (Ljung, 1999; Soderstrom Stoica, 1989), the fundamental problem with closed-loop data s the correlation between the unmeasurable noise and the input. his is true for traditional closed-loop identification approaches