Analysis of fractional delay systems of retarded and neutral type
type: Item
instance of: scholarly article
title: Analysis of fractional delay systems of retarded and neutral type
zbMATH Open document ID: 1007.93065
DOI: 10.1016/S0005-1098(01)00306-5
published in: Automatica
publication date: 2002-09-05T00:00:00Z
review text: The authors study fractional systems with scalar transfer function given by \[ P(s)=\frac{\sum_{i=1}^{n_2} q_i(s) e^{-\beta_i s}}{\sum_{i=1}^{n_1} p_i(s) e^{-\gamma_i s}}, \] where \(0=\gamma_0<\gamma_1<\cdots <\gamma_{n_1}\), \(0=\beta_0<\beta_1<\cdots <\beta_{n_2}\), the \(p_i\) being polynomials of the form \(\sum a_ks^{\alpha_k}\) with \(\alpha_k\in\mathbb R_+\) and the \(q_i\) being polynomials of the form \(\sum b_ks^{\delta_k}\) with \(\delta_k\in\mathbb R_+\). In order to analyse these systems, a frequency-domain approach is taken. The first main results provide a BIBO-stability analysis, which is in general quite difficult to perform since the impulse response of such a system cannot usually be written down explicitly, and the transfer function has a branch point on the imaginary axis. In particular, the BIBO stability of retarded and neutral fractional systems is related to the location of their poles. Further, sufficient conditions for nuclearity are given.
reviewed by: Birgit Jacob
Mathematics Subject Classification ID: 93D25
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 47B25
Mathematics Subject Classification ID: 93C80
zbMATH DE Number: 1797092
zbMATH Keywords: delay system
zbMATH Keywords: fractional system
zbMATH Keywords: BIBO stability
zbMATH Keywords: nuclearity
zbMATH Keywords: Hankel operator
zbMATH Keywords: frequency-domain approach
zbMATH Keywords: neutral systems
zbMATH Keywords: poles
Wikidata QID: Q56319398
author: Catherine Bonnet
author: Jonathan R. Partington
MaRDI profile type: Publication
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full work available at URL: s0005-1098(01)00306-5
OpenAlex ID: W1996430332
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description: scientific article; zbMATH DE number 1797092