Power-law stability of Hausdorff derivative nonlinear dynamical systems

The power law decay is widely observed in lab experiments and field observations. The Power-law stability, however, has little been reported in the literature. In this study, the definition of the Power-law stability is proposed, and then via the Lyapunov direct method, the Power-law stability of no...

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Bibliographic Details
Published inInternational journal of systems science Vol. 51; no. 4; pp. 601 - 607
Main Authors Hu, D. L., Chen, W., Sun, H. G.
Format Journal Article
LanguageEnglish
Published London Taylor & Francis 11.03.2020
Taylor & Francis Ltd
Subjects
Dynamic stability
Dynamical systems
fractal comparison principle
fractal Lyapunov direct method
Hausdorff derivative
Liapunov direct method
Nonlinear systems
Power law
Power-law stability
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Summary:The power law decay is widely observed in lab experiments and field observations. The Power-law stability, however, has little been reported in the literature. In this study, the definition of the Power-law stability is proposed, and then via the Lyapunov direct method, the Power-law stability of nonlinear dynamical systems based on the Hausdorff derivative is investigated. Furthermore, the fractal comparison principle is introduced to obtain the stability conditions for the dynamical systems of this type. Finally, two examples are given to elucidate the notion of Power-law stability.
ISSN:0020-7721
1464-5319
DOI:10.1080/00207721.2020.1737262