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Additional info for Advances in Theory and Applications : System Identification and Adaptive Control, Part 2
Tant for numerical reasons. It is impor It guarantees that if the data are informative enough, the parameter estimation problem will be well posed, since different Θ yield different I/O properties. The definition we have adopted is by no means unique. , , , ). Other definitions are based on the Kullback-Leibler information or on the theory of estimable functions Csee [35,36]). Notice finally that the term "structural identifiability" has a different meaning in econometrics . IV.
This particular V is called the generic neighborhood, because generically a system will have Kronecker indices n, , , + 1 = · · · = η p + 1 for 1 = ··· = n q = η q+1 some q. Hence, in practice, the generic neighborhood (and its corresponding canonical parametrization) is sufficient to repre sent almost any system. However, other nongeneric y's (and their corresponding parametrizations) might be preferred for numerical reasons. For the generic μ, d(y) = n(p + s ) ; the other V are mapped into spaces of lower dimension.
An alternative is to cover S(n) by disjoint sub sets V , which can again be coordinatized by nonoverlapping coordinate systems. These will give rise to the somewhat sim pler canonical SS, MFD, and ARMAX forms. Definition 3. the subset of U for which the μ rows (34) specified by μ are the first n linearly independent J We call V μ rows of H, [K]. i, °° Since the row r. +1n ' l basis rows above it, (35) is replaced by n. P il :. +l ^ zL ijl jl 1 j=l 1=1 where n. , p, if i < j, y — /\ min(n. ) (39) if J ' i > j.