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

    Fei Wang Info
    Yongqing Yang Info

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.

Keywords:

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

Share

Published in Issue
July 3, 2017
Abstract Views
977

View article in other formats

CrossMark check

CrossMark logo

Published

2017-07-03

Issue

Section

Articles

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

Share