Abstract
This paper investigates the impulsive synchronization scheme of fractional-order chaotic systems with actuator saturation and control gain error. Based on the theory of fractional order system and impulsive differential system, discontinuous Lyapunov stability and matrix inequality approach, some new sufficient conditions are derived to guarantee the impulsive synchronization of a general class of fractional order chaotic systems. It is worth mentioning that the actuator saturation and control gain error are discussed simultaneously, which is more rigorous and practical in real systems. Finally, some simulation results verify the correctness and effectiveness of the theoretical results.
Highlights
In the past few decades, the synchronization scheme for a myriad of chaotic systems has been wildly applied to many occasions, such as neural networks [1], mechanical systems [2] and data transmission privacy [3]
It should be noted that the impulsive control approach, one discontinuous control protocol, has special advantages over the above continuous ones
It is obviously concluded that the impulsive approach can obtain higher robustness and lower control cost in practical applications than the continuous control methods [17]– [20]
Summary
In the past few decades, the synchronization scheme for a myriad of chaotic systems has been wildly applied to many occasions, such as neural networks [1], mechanical systems [2] and data transmission privacy [3]. In [29], the robust synchronization case of the fractional order unified systems was studied by the linear control approach. In [31], the complete synchronization case of the commensurate fractional order systems with sliding mode control approach was studied. The adaptive synchronization of fractional order chaotic systems with uncertain system parameters via fuzzy sliding mode control approach was explored in [32]. In [41], the fuzzy adaptive control scheme of nonlinear fractional-order chaotic systems with unknown control gain sign was studied. Motivated by the above discussions, this paper mainly investigates the impulsive synchronization case of nonlinear fractional-order chaotic systems with actuator saturation and control gain error, which goes deep into investigation firstly in this paper.
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