## A unifying construction of orthonormal bases for system identifications.(English)Zbl 0874.93034

The author construct general, very simple, and complete orthonormal bases for system identification, which can encompass the previously studied orthonormal bases, such as the Laguerre base and the two-parameter Kautz base, as restrictive special cases, by a construction which is essentially a Gauss-Schmidt procedure. Moreover, the unifying basis vectors constructed in the paper provide arbitrary pole placement according to the prior information a user wishes to inject. Results characterizing the completeness of the bases in $$H_2(T)$$ are given and the accuracy properties of models estimated using the above-mentioned bases is studied.

### MSC:

 93B30 System identification 42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis 93B55 Pole and zero placement problems
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