New integral inequalities and asymptotic stability of fractional-order systems with unbounded time delay

The stability analysis of fractional-order systems with unbounded delay remains an open problem. In this paper, we firstly explore two new integral inequalities. Using these two integral inequalities obtained, the Halanay inequality with unbounded delay is extended to Caputo fractional-order case an...

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Bibliographic Details
Published in:Nonlinear dynamics 2018-10, Vol.94 (2), p.1523-1534
Main Authors: He, Bin-Bin, Zhou, Hua-Cheng, Kou, Chun-Hai, Chen, YangQuan
Format: Article
Language:English
Subjects:
Asymptotic properties
Automotive Engineering
Classical Mechanics
Control
Control systems
Delay
Dynamical Systems
Engineering
Inequalities
Integrals
Mechanical Engineering
Original Paper
Stability analysis
Time lag
Vibration
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Summary:The stability analysis of fractional-order systems with unbounded delay remains an open problem. In this paper, we firstly explore two new integral inequalities. Using these two integral inequalities obtained, the Halanay inequality with unbounded delay is extended to Caputo fractional-order case and Riemann–Liouville fractional-order case. Finally, several examples are presented to illustrate the effectiveness and applicability of the fractional Halanay inequalities in obtaining the asymptotic stability conditions of fractional-order systems with unbounded delay.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-018-4439-z