Publication detail

Impulse response of commensurate fractional-order systems: multiple complex poles

BIOLEK, D. GARRAPPA, R. BIOLKOVÁ, V.

Original Title

Impulse response of commensurate fractional-order systems: multiple complex poles

Type

journal article in Web of Science

Language

English

Original Abstract

The impulse response of a fractional-order system with the transfer function s(delta)/[(s(alpha) - a)(2) + b(2)](n), where n is an element of N, a is an element of R, b is an element of R+, alpha is an element of R+, delta is an element of R, is derived via real and imaginary parts of two-parameter Mittag-Leffler functions and their derivatives. With the aid of a robust algorithm for evaluating these derivatives, the analytic formulas can be used for an effective transient analysis of fractional-order systems with multiple complex poles. By some numerical experiments it is shown that this approach works well also when the popular SPICE-family simulating programs fail to converge to a correct solution.

Keywords

Fractional calculus; Mittag-Leffler functions; Laplace transform; Complex poles; Commensurate systems; Impulse response

Authors

BIOLEK, D.; GARRAPPA, R.; BIOLKOVÁ, V.

Released

14. 9. 2022

Publisher

Springer Nature

Location

LONDON

ISBN

1311-0454

Periodical

Fractional Calculus and Applied Analysis

Year of study

25

Number

5

State

Republic of Bulgaria

Pages from

1837

Pages to

1851

Pages count

15

URL

https://link.springer.com/article/10.1007/s13540-022-00086-4

BibTex

@article{BUT179289,
  author="Dalibor {Biolek} and Roberto {Garrappa} and Viera {Biolková}",
  title="Impulse response of commensurate fractional-order systems: multiple complex poles",
  journal="Fractional Calculus and Applied Analysis",
  year="2022",
  volume="25",
  number="5",
  pages="1837--1851",
  doi="10.1007/s13540-022-00086-4",
  issn="1311-0454",
  url="https://link.springer.com/article/10.1007/s13540-022-00086-4"
}