Wmatrix and the geometry of model equivalence and reduction

The wmatrix is shown to contain valuable information on the geometry of the dynamical behaviour of linear dynamical systems. Certain known results involving the wmatrix and new results, which demonstrate the importance of the Wmatrix in the equivalence and reduction of models, are presented. The concept of best subspaces is central to the problem of model reduction. It is shown that, for impulse inputs, the best subspace may be specified in terms of the eigenstructure of tne Wmatrix. The conditioning of a system is defined and investigated, and it is found to be determined by the W matrix. For white Gaussian noise disturbances, the correlation ellipsoid is defined and is given in terms of the Wmatrix. The best subspaces are reinterpreted in terms of the correlation ellipsoid. The minimum variance estimation problem in the context of inexact models is considered. Finally, an information theoretic functional for the model reduction problem is investigated.