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Laguerre series approximation of infinite dimensional systems. (English) Zbl 0717.93028

Summary: Laguerre-Fourier approximations of stable systems are shown to exhibit many desirable properties for various classes of infinite dimensional systems. Specifically, time domain supremum and \(L^ 1\) norm convergence results, and frequency domain \(H^{\infty}\) norm convergence results, are given for Laguerre-Fourier approximations. It is also shown that the theory of Laguerre polynomials solves explicitly the problem of determining Laguerre-Fourier approximations for a large class of delay systems. Furthermore, it is believed that these results are important for the study of orthonormal series identification as a general technique for identification of infinite dimensional systems.

MSC:

93B99 Controllability, observability, and system structure
93B30 System identification
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
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