Detail publikačního výsledku

Basis Functions for a Transient Analysis of Linear Commensurate Fractional-Order Systems

BIOLEK, D.; BIOLKOVÁ, V.; KOLKA, Z.; BIOLEK, Z.

Originální název

Basis Functions for a Transient Analysis of Linear Commensurate Fractional-Order Systems

Anglický název

Basis Functions for a Transient Analysis of Linear Commensurate Fractional-Order Systems

Druh

Článek WoS

Originální abstrakt

In this paper, the possibilities of expressing the natural response of a linear commensurate fractional-order system (FOS) as a linear combination of basis functions are analyzed. For all possible types of s(& alpha;)-domain poles, the corresponding basis functions are found, the kernel of which is the two-parameter Mittag-Leffler function E-& alpha;(,& beta;), & beta; = & alpha;. It is pointed out that there are mutually unambiguous correspondences between the basis functions of FOS and the known basis functions of the integer-order system (IOS) for & alpha; = 1. This correspondence can be used to algorithmically find analytical formulas for the impulse responses of FOS when the formulas for the characteristics of IOS are known. It is shown that all basis functions of FOS can be generated with Podlubny's function of type & epsilon;(k) (t, c; & alpha;, & alpha;), where c and k are the corresponding pole and its multiplicity, respectively.

Anglický abstrakt

In this paper, the possibilities of expressing the natural response of a linear commensurate fractional-order system (FOS) as a linear combination of basis functions are analyzed. For all possible types of s(& alpha;)-domain poles, the corresponding basis functions are found, the kernel of which is the two-parameter Mittag-Leffler function E-& alpha;(,& beta;), & beta; = & alpha;. It is pointed out that there are mutually unambiguous correspondences between the basis functions of FOS and the known basis functions of the integer-order system (IOS) for & alpha; = 1. This correspondence can be used to algorithmically find analytical formulas for the impulse responses of FOS when the formulas for the characteristics of IOS are known. It is shown that all basis functions of FOS can be generated with Podlubny's function of type & epsilon;(k) (t, c; & alpha;, & alpha;), where c and k are the corresponding pole and its multiplicity, respectively.

Klíčová slova

Mittag-Leffler function; commensurate fractional-order system; basis function; impulse response

Klíčová slova v angličtině

Mittag-Leffler function; commensurate fractional-order system; basis function; impulse response

Autoři

BIOLEK, D.; BIOLKOVÁ, V.; KOLKA, Z.; BIOLEK, Z.

Rok RIV

2024

Vydáno

13.07.2023

Nakladatel

MDPI

Místo

BASEL

ISSN

1999-4893

Periodikum

Algorithms

Svazek

16

Číslo

7

Stát

Švýcarská konfederace

Strany od

1

Strany do

22

Strany počet

22

URL

https://www.mdpi.com/1999-4893/16/7/335

Plný text v Digitální knihovně

http://hdl.handle.net/11012/244995

BibTex

@article{BUT184376,
  author="Dalibor {Biolek} and Viera {Biolková} and Zdeněk {Kolka} and Zdeněk {Biolek}",
  title="Basis Functions for a Transient Analysis of Linear Commensurate Fractional-Order Systems",
  journal="Algorithms",
  year="2023",
  volume="16",
  number="7",
  pages="1--22",
  doi="10.3390/a16070335",
  url="https://www.mdpi.com/1999-4893/16/7/335"
}

Dokumenty

algorithms-16-00335-v3