Synthesis of complete rational orthonormal bases with prescribed asymptotic order

Akcay H.

AUTOMATICA, vol.37, no.4, pp.559-564, 2001 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 4
  • Publication Date: 2001
  • Doi Number: 10.1016/s0005-1098(00)00187-4
  • Journal Name: AUTOMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.559-564
  • Keywords: orthonormal bases, completeness, asymptotic order, Toeplitz determinants, generalized Laguerre functions, CONTINUOUS-TIME SYSTEMS, LINEAR DYNAMICAL-SYSTEMS, IDENTIFICATION, LAGUERRE
  • Anadolu University Affiliated: No

Abstract

In this paper, a method to construct complete rational orthonormal model sets with prescribed asymptotic order is presented for continuous-time systems. Two special cases that illustrate the application of the method are studied. In the first case, this method is shown to produce the generalized Laguerre functions which form a complete model set for H-2 and have asymptotic order two. In both eases, this method is equivalent to calculating Toeplitz determinants generated by a rational function. The latter problem is reduced to finding solution of a linear finite-difference equation. (C) 2001 Elsevier Science Ltd. All rights reserved.