Publication detail

Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case

KISELA, T. ČERMÁK, J.

Czech title

Asymptotická stabilita dynamických rovnic se dvěma zlomkovými členy: Spojitý versus diskrétní případ

English title

Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case

Type

journal article in Web of Science

Language

en

Original abstract

The paper discusses asymptotic stability conditions for the linear fractional difference equation ∇αy(n) + a∇βy(n) + by(n) = 0 with real coefficients a, b and real orders α > β > 0 such that α/β is a rational number. For given α, β, we describe various types of discrete stability regions in the (a, b)-plane and compare them with the stability regions recently derived for the underlying continuous pattern Dαx(t) + aDβx(t) + bx(t) = 0 involving two Caputo fractional derivatives. Our analysis shows that discrete stability sets are larger and their structure much more rich than in the case of the continuous counterparts.

Czech abstract

Článek diskutuje podmínky pro asymptotickou stabilitu lineární diferenční rovnice ∇αy(n) + a∇βy(n) + by(n) = 0 s reálnými koeficienty a, b a reálnými řády α > β > 0 takovými, že α/β je racionální číslo. Pro daná α, β, popíšeme různé typy diskrétních oblastí stability v rovině (a,b) a srovnáme je se oblastmi stability nedávno odvozenými pro odpovídající spojitý model Dαx(t) + aDβx(t) + bx(t) = 0 obsahující dvě Caputovy zlomkové derivace. Naše analýza ukazuje, že diskrétní oblasti stability jsou větší a jejich struktura bohatší než v odpovídajích spojitých případech.

English abstract

The paper discusses asymptotic stability conditions for the linear fractional difference equation ∇αy(n) + a∇βy(n) + by(n) = 0 with real coefficients a, b and real orders α > β > 0 such that α/β is a rational number. For given α, β, we describe various types of discrete stability regions in the (a, b)-plane and compare them with the stability regions recently derived for the underlying continuous pattern Dαx(t) + aDβx(t) + bx(t) = 0 involving two Caputo fractional derivatives. Our analysis shows that discrete stability sets are larger and their structure much more rich than in the case of the continuous counterparts.

Keywords in Czech

zlomková diferenciální rovnice; zlomková diferenční rovnice; asymptotická stabilita; zlomkové Schurovo-Cohnovo kritérium

Keywords in English

fractional differential equation; fractional difference equation; asymptotic stability; fractional Schur-Cohn criterion

RIV year

2015

Released

30.04.2015

ISSN

1311-0454

Volume

18

Number

2

Pages from–to

437–458

Pages count

22

BIBTEX


@article{BUT115854,
  author="Tomáš {Kisela} and Jan {Čermák},
  title="Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case",
  year="2015",
  volume="18",
  number="2",
  month="April",
  pages="437--458",
  issn="1311-0454"
}