Abstract
This paper studies the finite-time synchronization of fractional-order chaotic systems with different structures under parameter disturbance and external disturbance. We put forward a fractional-order controller that can achieve the finite-time synchronization of any-order fractional-order chaotic systems under stochastic disturbances. This controller has good robustness and anti-interference performance. With the concept of the finite-time stability theory given, some judgment criterions for the synchronization of fractional-order chaotic systems are proved. This method can not only make the error systems have a faster convergence rate but also can be implemented in engineering easily. The numerical simulations of two specific examples demonstrate the effectiveness of the method. At the same time, the synchronised time of finite-time synchronization is shorter and faster than the complete synchronization and the time can be adjusted according to the parameters in the controller.
Highlights
The development history of fractional and integer calculus is not much different, it turns out that fractional calculus is of great significance to express the model we are studying
This paper studies the finite-time synchronization of fractional-order chaotic systems with different structures under parameter disturbance and external disturbance
We have studied the finite-time synchronization of fractional-order chaotic systems with different structures under parameter disturbance and external disturbance
Summary
The development history of fractional and integer calculus is not much different, it turns out that fractional calculus is of great significance to express the model we are studying. Literatures [31] [32] [33] have solved the synchronization of fractional-order chaotic systems under random disturbance, but they only considered one of the above three disturbances. If they can consider multiple disturbances, it has more practical significance. Literatures [34] [35] [36] consider the case of multiple disturbances, the object of their research is the integer order chaotic system In response to this situation, we are going to consider the synchronization of fractional-order chaotic systems under two kinds of disturbances, namely para-. Where α ∈ (0,1) and Q is an arbitrary n order positive definite matrix
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