Fractional Order Barbalat’s Lemma and its Applications in the Stability of Fractional Order Nonlinear Systems
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, stabilityHow to Cite
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Copyright (c) 2017 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2017 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.