nach oben

Fuzzy Optimization and Decision Making

Erschienen in:

07.02.2020

Finite-time stability of uncertain fractional difference equations

verfasst von: Qinyun Lu, Yuanguo Zhu

Erschienen in: Fuzzy Optimization and Decision Making | Ausgabe 2/2020

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

Uncertain fractional difference equations may preferably describe the behavior of the systems with the memory effect and discrete feature in the uncertain environment. So it is of great significance to investigate their stability. In this paper, the concept of finite-time stability almost surely for uncertain fractional difference equations is introduced. A finite-time stability theorem is then stated by Mittag–Leffler function and proved by a generalized Gronwall inequality on a finite time. Some examples are finally presented to illustrate the validity of our results.

Vorheriger Artikel Option implied moments obtained through fuzzy regression

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 "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
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

Amato, F., Ariola, M., & Cosentino, C. (2010). Finite-time stability of linear time-varying systems: analysis and controller design. IEEE Transactions on Automatic Control, 55(4), 1003–1008.MathSciNetCrossRef

Amato, F., Tommasi, G. D., & Pironti, A. (2013). Necessary and sufficient conditions for finite-time stability of impulsive dynamical linear systems. Automatica, 49(8), 2546–2550.MathSciNetCrossRef

Atici, F. M., & Eloe, P. W. (2007). A transform method in discrete fractional calculus. Integral and Finite Difference Inequalities and Applications, 2(2), 165–176.MathSciNet

Atici, F. M., & Eloe, P. W. (2009). Initial value problems in discrete fractional calculus. Proceeding of American Mathematical Society, 137(4), 981–989.MathSciNetMATH

Bhat, S. P., & Bernstein, D. S. (1997). Finite-time stability of homogeneous systems. Proceedings of the American Control Conference, 4, 2513–2514.

Koeller, R. C. (1984). Application of fractional calculus to the theory of viscoelasticity. Journal of Applied Mechanics, 51(2), 299–307.MathSciNetCrossRef

Lazarevi, M. P. (2006). Finite time stability analysis of PD\(^\alpha \) fractional control of robotic time-delay systems. Mechanics Research Communications, 33, 269–279.MathSciNetCrossRef

Lazarevi, M. P., & Spasi, M. A. (2009). Finite-time stability analysis of fractional order time delay systems: Gronwall’s approach. Mathematical and Computer Modelling, 49, 475–481.MathSciNetCrossRef

Liu, B. (2007). Uncertainty theory (2nd ed.). Berlin: Springer.MATH

Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.

Liu, B. (2010). Uncertainty theory: a branch of mathematics for modeling human uncertainty. Berlin: Springer.CrossRef

Lu, Q., Zhu, Y., & Lu, Z. (2019). Uncertain fractional forward difference equations for Riemann–Liouville type. Advances in Difference Equations, 2019(147), 1–11.MathSciNetMATH

Lu, Z., Yan, H., & Zhu, Y. (2019). European optition pricing model based on uncertain fractional differential equation. Fuzzy Optimization and Decision Making, 18(2), 199–217.MathSciNetCrossRef

Lu, Z., & Zhu, Y. (2019). Numerical approach for solution to an uncertain fractional differential equation. Applied Mathematics and Computation, 343, 137–148.MathSciNetCrossRef

Magin, R. L. (2010). Fractional calculus models of complex dynamics in biological tissues. Computers and Mathematics with Applications, 59(5), 1586–1593.MathSciNetCrossRef

Michel, A. N., & Wu, S. H. (1969). Stability of discrete systems over a finite interval of time. International Journal of Control, 9(6), 679–693.MathSciNetCrossRef

Perruquetti, W., Moulay, E., & Dambrine, M. (2008). Finite-time stability and stabilization of time-delay systems. Systems and Control Letters, 57(7), 561–566.MathSciNetCrossRef

Phat, V. N., & Thanh, N. T. (2018). New criteria for finite-time stability of nonlinear fractional-order delay systems: a Gronwall inequality approach. Applied Mathematics Letters, 83, 169–175.MathSciNetCrossRef

Tien, D. N. (2013). Fractional stochastic differential equations with applications to finance. Journal of Mathematical Analysis and Applications, 397(1), 334–348.MathSciNetCrossRef

Wu, G., Baleanu, D., & Zeng, S. (2018). Finite-time stability of discrete fractional delay systems: Gronwall inequality and stability criterion. Communications in Nonlinear Science and Numerical Simulation, 57, 299–308.MathSciNetCrossRef

Yin, J., Khoo, S., Man, Z., et al. (2011). Finite-time stability and instability of stochastic nonlinear systems. Automatica, 47(12), 2671–2677.MathSciNetCrossRef

Zhu, Y. (2015a). Uncertain fractional differential equations and an interest rate model. Mathematical Methods in the Applied Sciences, 38(15), 3359–3368.MathSciNetCrossRef

Zhu, Y. (2015b). Existence and uniqueness of the solution to uncertain fractional differential equation. Journal of Uncertainty Analysis and Applications, 3(1), 1–11.CrossRef

Titel: Finite-time stability of uncertain fractional difference equations
verfasst von: Qinyun Lu
Yuanguo Zhu
Publikationsdatum: 07.02.2020
Verlag: Springer US
Erschienen in: Fuzzy Optimization and Decision Making / Ausgabe 2/2020
Print ISSN: 1568-4539
Elektronische ISSN: 1573-2908
DOI: https://doi.org/10.1007/s10700-020-09318-9

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

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

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 2/2020

Harmonizing two approaches to fuzzy random variables

On weak consistency of interval additive reciprocal matrices

Mathematical programming approach to formulate intuitionistic fuzzy regression model based on least absolute deviations

Option implied moments obtained through fuzzy regression

A scalarization method for fuzzy set optimization problems