Robust Synchronization of Uncertain Fractional Order Chaotic Systems

2015 ◽  
Vol E98.A (10) ◽  
pp. 2109-2116 ◽  
Author(s):  
Junhai LUO ◽  
Heng LIU ◽  
Jiangfeng YANG
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Robust Synchronization

scholarly journals Robust Synchronization Controller Design for a Class of Uncertain Fractional Order Chaotic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Lin Wang ◽  
Chunzhi Yang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Closed Loop ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Closed Loop System ◽  
Synchronization Problem ◽  
Robust Synchronization ◽  
Lyapunov Stability Criterion ◽  
Theoretical Results

Synchronization problem for a class of uncertain fractional order chaotic systems is studied. Some fundamental lemmas are given to show the boundedness of a complicated infinite series which is produced by differentiating a quadratic Lyapunov function with fractional order. By using the fractional order extension of the Lyapunov stability criterion and the proposed lemma, stability of the closed-loop system is analyzed, and two sufficient conditions, which can enable the synchronization error to converge to zero asymptotically, are driven. Finally, an illustrative example is presented to confirm the proposed theoretical results.

Robust synchronization of perturbed Chen’s fractional-order chaotic systems

2011 ◽  
Vol 16 (2) ◽  
pp. 1044-1051 ◽  
Author(s):  
Mohammad Mostafa Asheghan ◽  
Mohammad Taghi Hamidi Beheshti ◽  
Mohammad Saleh Tavazoei
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Robust Synchronization

scholarly journals Dynamic Behavior Analysis and Robust Synchronization of a Novel Fractional-Order Chaotic System with Multiwing Attractors

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Chenhui Wang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Chaotic Attractors ◽  
Stability Criteria ◽  
Minimum Order ◽  
3 Dimensional ◽  
Robust Synchronization ◽  
New Type ◽  
The Stability

To enrich the types of multiwing chaotic attractors in fractional-order chaotic systems (FOCSs), a new type of 3-dimensional FOCSs is designed in this study. The most important contribution of this FOCS consists in the coexistence of multiple multiwing chaotic attractors, including 2-wing, 3-wing, and 4-wing attractors. It is also indicated that the minimum order that the system can exhibit chaotic behavior is 0.84. Then, based on certain fractional stability criteria, a robust synchronization controller is derived for this kind of FOCSs with multiwing chaotic attractors and parametric uncertainties, and the stability of the synchronization error is proven strictly. Meanwhile, the theoretical analysis is tested by simulation results.

scholarly journals Robust Synchronization of Fractional-Order Uncertain Chaotic Systems Based on Output Feedback Sliding Mode Control

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 599 ◽  
Author(s):  
Chao Song ◽  
Shumin Fei ◽  
Jinde Cao ◽  
Chuangxia Huang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Control Technique ◽  
Unknown Parameters ◽  
Mode Control ◽  
Robust Synchronization ◽  
The Stability ◽  
Output Information

This paper mainly focuses on the robust synchronization issue for drive-response fractional-order chaotic systems (FOCS) when they have unknown parameters and external disturbances. In order to achieve the goal, the sliding mode control scheme only using output information is designed, and at the same time, the structures of a sliding mode surface and a sliding mode controller are also constructed. A sufficient criterion is presented to ensure the robust synchronization of FOCS according to the stability theory of the fractional calculus and sliding mode control technique. In addition, the result can be applied to identical or non-identical chaotic systems with fractional-order. In the end, we build two practical examples to illustrate the feasibility of our theoretical results.

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