Share:


Fractional Order Barbalat’s Lemma and its Applications in the Stability of Fractional Order Nonlinear Systems

    Fei Wang Affiliation
    ; Yongqing Yang Affiliation

Abstract

This paper investigates fractional order Barbalat’s lemma and its applications for the stability of fractional order nonlinear systems with Caputo fractional derivative at first. Then, based on the relationship between Caputo fractional derivative and Riemann-Liouville fractional derivative, fractional order Barbalat’s lemma with Riemann-Liouville derivative is derived. Furthermore, according to these results, a set of new formulations of Lyapunov-like lemmas for fractional order nonlinear systems are established. Finally, an example is presented to verify the theoretical results in this paper.

Keyword : fractional order system, nonlinear differential equation, stability

How to Cite
Wang, F., & Yang, Y. (2017). Fractional Order Barbalat’s Lemma and its Applications in the Stability of Fractional Order Nonlinear Systems. Mathematical Modelling and Analysis, 22(4), 503-513. https://doi.org/10.3846/13926292.2017.1329755
Published in Issue
Jul 3, 2017
Abstract Views
407
PDF Downloads
492
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.