Finite-time stability of discrete fractional delay systems: Gronwall inequality and stability criterion

•A generalized Gronwall inequality is given on finite time domain.•Finite-time stability of discrete fractional delay systems is discussed.•New finite-time stability criterion is provided. This study investigates finite-time stability of Caputo delta fractional difference equations. A generalized Gr...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2018-04, Vol.57, p.299-308
Main Authors: Wu, Guo–Cheng, Baleanu, Dumitru, Zeng, Sheng–Da
Format: Article
Language:English
Subjects:
Difference equations
Differential equations
Discrete element method
Discrete time control
Finite-time stability
Fractional difference equations
Image processing systems
Mathematical analysis
Stability criteria
Time scale
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Summary:•A generalized Gronwall inequality is given on finite time domain.•Finite-time stability of discrete fractional delay systems is discussed.•New finite-time stability criterion is provided. This study investigates finite-time stability of Caputo delta fractional difference equations. A generalized Gronwall inequality is given on a finite time domain. A finite-time stability criterion is proposed for fractional differential equations. Then the idea is extended to the discrete fractional case. A linear fractional difference equation with constant delays is considered and finite-time stable conditions are provided. One example is numerically illustrated to support the theoretical result.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2017.09.001