Continuous-time stable and unstable system modelling with orthonormal basis functions

Akcay H.

INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, vol.10, no.6, pp.513-531, 2000 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 6
  • Publication Date: 2000
  • Journal Name: INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.513-531
  • Keywords: continuous time, orthonormal basis functions, completeness, Fourier series, LINEAR DYNAMICAL-SYSTEMS, ROBUST IDENTIFICATION, CONSTRUCTION
  • Anadolu University Affiliated: No

Abstract

In this paper, model sets for linear time-invariant continuous-time systems which are spanned by fixed-pole orthonormal bases are investigated. The obtained model sets are shown to be complete in the Lebesque spaces L-p (1 < p < infinity) and in C, the space of complex-valued functions that are continuous on the extended imaginary axis. The L-p norm error bounds for estimating systems in L-p by the partial sums of the Fourier series formed by the orthonormal functions are computed for the case 1 < p < infinity. Some inequalities on the l(p) means of the Fourier coefficients are also derived. These results have application in estimation and model reduction of stable and unstable continuous-time linear time-invariant systems. A numerical example illustrates the use of the basis functions for the approximation of unstable infinite-dimensional dynamics. Copyright (C) 2000 John Wiley & Sons, Ltd.