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T. Ribarits, M. Deistler:
"Data driven local coordinates: some new topological and geometrical results";
Talk: 15th IFAC world congress, Barcelona; 2002-07-21 - 2002-07-26; in: "Proceedings of the 15th IFAC world congress", (2002).

Certain topological and geometrical properties of data driven local coordinates (DDLC) for state-space systems as introduced in (Wolodkin et al., 1997) and (McKelvey and Helmersson, 1999) are derived. First the special case of SISO systems with McMillan degree n=1 is discussed in order to provide some insights into the geometry of the DDLC construction. Then for the MIMO case with general n it is shown that the set of transfer functions corresponding to the parameter space contains a nonvoid open subset of the manifold of transfer functions of order n and that the estimation problem is locally well posed. Moreover, it is stated that the parameter space always contains points corresponding to non minimal systems and a result on the number of disconnected components of the equivalence classes in the space R^{n^2+n(m+s)} (obtained by an embedding of the system matrices (A,B,C)) concludes this contribution.