Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Existence of Solutions of Abstract Fractional Impulsive Integrodifferential Equations of Sobolev Type Kapitel lesen Erstes Kapitel lesen

2017 | OriginalPaper | Buchkapitel

Stability Analysis for the New Model of Fractional Discrete-Time Linear State-Space Systems

verfasst von : Andrzej Ruszewski

Erschienen in: Theory and Applications of Non-integer Order Systems

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In the paper the problem of asymptotic stability of fractional discrete-time linear systems described by the new model are addressed. Necessary and sufficient conditions for asymptotic stability are established. It is shown that location of all eigenvalues of the state matrix in the stability region is necessary and sufficient for asymptotic stability. The parametric description of boundary of this region is given. The considerations are illustrated by numerical examples.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Relative Controllability of Nonlinear Fractional Delay Dynamical Systems with Time Varying Delay in Control
Nächstes Kapitel Fractional Differential-Algebraic Systems with Delay: Computation of Final Dimension Initial Conditions and Inputs for Given Outputs
Literatur
1.
Ahn, H.-S., Chen, Y.Q.: Necessary and sufficient stability condition of fractional-order interval linear systems. Automatica 44(11), 2985–2988 (2008)MathSciNetCrossRefMATH
2.
Busłowicz, M.: Robust stability of positive discrete-time linear systems of fractional order. Bull. Pol. Acad. Tech. 58(4), 567–572 (2010)MATH
3.
Busłowicz, M.: Stability of state-space models of linear continuous-time fractional order systems. Acta Mech. Autom. 5(2), 15–22 (2011)
4.
Busłowicz, M.: Simple analytic conditions for stability of fractional discrete-time linear systems with diagonal state matrix. Bull. Pol. Acad. Tech. 60(4), 809–814 (2012)
5.
Busłowicz, M.: Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders. Bull. Pol. Acad. Tech. 60(2), 279–284 (2012)
6.
Busłowicz, M.: Stability conditions for linear continuous-time fractional-order state-delayed systems. Bull. Pol. Acad. Tech. 64(2), 3–7 (2016)
7.
Busłowicz, M., Kaczorek, T.: Simple conditions for practical stability of linear positive fractional discrete-time linear systems. Int. J. Appl. Math. Comput. Sci. 19(2), 263–269 (2009)MathSciNetMATH
8.
Busłowicz, M., Ruszewski, A.: Necessary and sufficient conditions for stability of fractional discrete-time linear state-space systems. Bull. Pol. Acad. Tech. 61(4), 779–786 (2013)
9.
Busłowicz, M., Ruszewski, A.: Robust stability check of fractional discrete-time linear systems with interval uncertainties. In: Latawiec, K.J., et al. (eds.) Advances in Modeling and Control of Non-integer Order Systems. Lecture Notes in Electrical Engineering, vol. 320, pp. 199–208. Springer, Switzerland (2014)
10.
Chen, Y.Q., Ahn, H.-S., Podlubny, I.: Robust stability check of fractional order linear time invariant systems with interval uncertainties. Signal Process. 86(10), 2611–2618 (2006)CrossRefMATH
11.
Dzieliński, A., Sierociuk, D.: Stability of discrete fractional state-space systems. J. Vib. Control 14(9–10), 1543–1556 (2008)MathSciNetCrossRefMATH
12.
Gryazina, E.N., Polyak, B.T., Tremba, A.A.: D-decomposition technique state-of-the-art. Autom. Remote Control 69(13), 1991–2026 (2008)MathSciNetCrossRefMATH
13.
Kaczorek, T., Ostalczyk, P.: Responses comparison of the two discrete-time linear fractional state-space models. Int. J. Control (2016, in press)
14.
Kaczorek, T.: Practical stability of positive fractional discrete-time systems. Bull. Pol. Acad. Tech. 56(4), 313–317 (2008)MathSciNet
15.
Kaczorek, T.: Selected Problems of Fractional Systems Theory. Springer, Berlin (2011)CrossRefMATH
16.
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)MATH
17.
Liao, Z., Peng, C., Li, W., Wang, Y.: Robust stability analysis for a class of fractional order systems with uncertain parameters. J. Franklin Inst. 348(6), 1101–1113 (2011)MathSciNetCrossRefMATH
18.
Monje, C., Chen, Y., Vinagre, B., Xue, D., Feliu, V.: Fractional-Order Systems and Controls. Springer, London (2010)CrossRefMATH
19.
Ostalczyk, P.: Epitome of the Fractional Calculus. Publishing Department of Technical University of Łódź, Łódź, Theory and Its Applications in Automatics (2008) (in Polish)
20.
Ostalczyk, P.: Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains. Int. J. Appl. Math. Comput. Sci. 22(3), 533–538 (2012)MathSciNetCrossRefMATH
21.
Petras, I.: Stability of fractional-order systems with rational orders: a survey. Fract. Calc. Appl. Anal. 12(3), 269–298 (2009)MathSciNetMATH
22.
Podlubny, I.: Fractional Differential Equations. Academic, San Diego (1999)MATH
23.
Ruszewski, R.: Practical stability and asymptotic stability of interval fractional discrete-time linear state-space system. In: Szewczyk, R., et al. (eds.) Recent Advances in Automation, Robotics and Measuring Techniques. Advances in Intelligent Systems and Computing, vol. 267, pp. 217–227. Springer, Switzerland (2014)CrossRef
24.
Sabatier, J., Agrawal, O.P., Machado, J.A.T. (eds.): Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, London (2007)MATH
25.
Stanisławski, R., Latawiec, K.J.: Stability analysis for discrete-time fractional-order LTI state-space systems. Part I: new necessary and sufficient conditions for asymptotic stability. Bull. Pol. Acad. Tech. 61(2), 353–361 (2013)
Metadaten
Titel
Stability Analysis for the New Model of Fractional Discrete-Time Linear State-Space Systems
verfasst von
Andrzej Ruszewski
Copyright-Jahr
2017
Buch
Theory and Applications of Non-integer Order Systems

Print ISBN: 978-3-319-45473-3

Electronic ISBN: 978-3-319-45474-0

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-45474-0_34

Neuer Inhalt

    Bildnachweise