Lyapunov stability criteria in terms of class K functions for Riemann–Liouville nabla fractional order systems

This paper focuses on the problem of stability analysis for Riemann–Liouville nabla fractional order systems. On one hand, a useful comparison principle is built and then a rigorous proof is constructed for the well-known Lyapunov stability criterion in terms of class K functions. On the other hand,...

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Bibliographic Details
Published in:ISA transactions 2022-12, Vol.131, p.137-145
Main Authors: Wei, Yiheng, Zhao, Xuan, Wei, Yingdong, Chen, YangQuan
Format: Article
Language:English
Subjects:
Asymptotic stability
Attractiveness
Boundedness
Class [formula omitted] functions
Fractional order systems
Gamma Rays
Lyapunov method
Neural Networks, Computer
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Summary:This paper focuses on the problem of stability analysis for Riemann–Liouville nabla fractional order systems. On one hand, a useful comparison principle is built and then a rigorous proof is constructed for the well-known Lyapunov stability criterion in terms of class K functions. On the other hand, the constraint of the Lyapunov function is refined using a positive constant γ4 or a sequence h(k), resulting two practical theorems. Finally, three illustrative examples are given to show the applicability of the proposed method. •A new and practical comparison principle is developed.•A strict proof is constructed for the Lyapunov criterion of asymptotic stability.•Two stability criteria are developed for such systems firstly.•The attractiveness criterion is less conservative than the existing one.
ISSN:0019-0578
1879-2022
DOI:10.1016/j.isatra.2022.05.008