A MULTIVARIABLE STEIGLITZ-MCBRIDE METHOD - STATIONARY-POINTS AND A-PRIORI ERROR BOUND

Citation
M. Mboup et al., A MULTIVARIABLE STEIGLITZ-MCBRIDE METHOD - STATIONARY-POINTS AND A-PRIORI ERROR BOUND, International Journal of Control, 68(1), 1997, pp. 125-153
Citations number
33
Categorie Soggetti
Controlo Theory & Cybernetics","Robotics & Automatic Control
ISSN journal
00207179
Volume
68
Issue
1
Year of publication
1997
Pages
125 - 153
Database
ISI
SICI code
0020-7179(1997)68:1<125:AMSM-S>2.0.ZU;2-V
Abstract
We present two dual versions of a multi-input/multi-output (MIMO) Stei glitz-McBride identification method, and give an analytic description of the set of the possible stationary points. As in the scalar case (R egalia and Mboup 1992, Regalia 1995), the description is given in term s of first-and second-order interpolation constraints on the model imp ulse response and covariance sequences, respectively. The constraints are related to the theory of M-Markov covariance equivalent realizatio ns and generalize the works of Inouye (1983) and King et al. (1988). I t is shown that the description is intimately connected to a class of first- and second-order matrix-valued interpolation problems of tangen tial Nevanlinna-Pick type. Such problems are studied by Alpay et al. ( 1996). We also examine the quality of the model furnished in reduced o rder cases, and show in particular that the mismodelling error at any stationary point of the method can be bounded in terms of the Hankel s ingular values of the unknown system. The bound so obtained compares f avourably with known bounds from L-2- and Hankel-norm model reduction.