Some results on the convergence of transfer function expansions on the Laguerre series

Rachid Malti (1) , Didier Maquin (1) , José Ragot (1)

1 CRAN - Centre de Recherche en Automatique de Nancy

When a transfer function is expanded on the basis of Laguerre filters, the question of how well does the expansion converge arises frequently. Beyond this problem, the convergence domain of the Laguerre series must be determined in the s-plane, as is usually done for the Laplace transform of time-domain functions. In the usual approach, this analysis is made in two complementary stages: first of all, the convergence conditions of Fourier (also called Laguerre or Laguerre-Fourier) coefficients is determined and then, based on the assumption that these coefficients are convergent, a worst-case-study is carried out to determine the convergence domain of the Laguerre series. A novel approach is proposed in this paper which drops away the coupling between the convergence of the Fourier coefficients and the convergence of the Laguerre series. Thus, necessary and sufficient conditions for Laguerre series convergence are computed. Laguerre functions are considered in their general definition : orthogonal w.r.t. an exponential weight function.

Domains: Automatic

Rachid Malti, Didier Maquin, José Ragot. Some results on the convergence of transfer function expansions on the Laguerre series. 5th European Control Conference, ECC'99, Aug 1999, Karlsruhe, Germany. pp.CDROM. ⟨hal-00283923⟩