Convergence of Laguerre impulse response approximation for noninteger order systems
type: Item
instance of: scholarly article
title: Convergence of Laguerre impulse response approximation for noninteger order systems
zbMATH Open document ID: 1400.42003
DOI: 10.1155/2016/9258437
author: Piotr Bania
author: Jerzy Baranowski
author: Marta Zagórowska
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: One of the most important issues in application of noninteger order systems concerns their implementation. One of the possible approaches is the approximation of convolution operation with the impulse response of noninteger system. In this paper, new results on the Laguerre Impulse Response Approximation method are presented. Among the others, a new proof of \(\mathcal{L}_1\) convergence of approximation is given, allowing less strict assumptions. Additionally, more general results are given including one regarding functions that are in the joint part of \(\mathcal{L}_1\) and \(\mathcal{L}_2\) spaces. The method was also illustrated with examples of use: analysis of ``fractional order lag'' system, application to noninteger order filters design, and parametric optimization of fractional controllers.
Mathematics Subject Classification ID: 42A10
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 93B15
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 6953762
Wikidata QID: Q59141042
describes a project that uses: CRONE
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/9258437
OpenAlex ID: W2511361931
cites work: Q4844958
cites work: Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review
cites work: Q4438501
cites work: Two direct Tustin discretization methods for fractional-order differentiator/integrator.
cites work: Fractional-order systems and controls. Fundamentals and applications
cites work: Design of FIR and IIR fractional order simpson digital integrators
cites work: Computation of fractional order derivative and integral via power series expansion and signal modelling
cites work: Improved digital rational approximation of the operator \(S^\alpha\) using second-order s-to-z transform and signal modeling
cites work: Diffusive representation of pseudo-differential time-operators
cites work: State space approximation for general fractional order dynamic systems
cites work: State variables and transients of fractional order differential systems
cites work: Stabilization of Wave Equation Using Standard/Fractional Derivative in Boundary Damping
cites work: Synthesis of fractional Laguerre basis for system approximation
cites work: Laguerre Polynomial Approximation of Fractional Order Linear Systems
cites work: On digital realizations of non-integer order filters
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
cites work: Selected problems of fractional systems theory.
cites work: Q3044222
description: scientific article; zbMATH DE number 6953762