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A generalized orthonormal basis for linear dynamical systems

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3 Author(s)
Heuberger, P.S.C. ; Mech. Eng. Syst. & Control Group, Delft Univ. of Technol., Netherlands ; Van den Hof, P.M.J. ; Bosgra, O.H.

In many areas of signal, system, and control theory, orthogonal functions play an important role in issues of analysis and design. In this paper, it is shown that there exist orthogonal functions that, in a natural way, are generated by stable linear dynamical systems and that compose an orthonormal basis for the signal space l2n . To this end, use is made of balanced realizations of inner transfer functions. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions, and give rise to an alternative series expansion of rational transfer functions. It is shown how we can exploit these generalized basis functions to increase the speed of convergence in a series expansion, i.e., to obtain a good approximation by retaining only a finite number of expansion coefficients. Consequences for identification of expansion coefficients are analyzed, and a bound is formulated on the error that is made when approximating a system by a finite number of expansion coefficients

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Automatic Control, IEEE Transactions on  (Volume:40 ,  Issue: 3 )