Abstract
A new fractional-order chaotic system is addressed in this paper. By applying the continuous frequency distribution theory, the indirect Lyapunov stability of this system is investigated based on sliding mode control technique. The adaptive laws are designed to guarantee the stability of the system with the uncertainty and external disturbance. Moreover, the modified generalized projection synchronization (MGPS) of the fractional-order chaotic systems is discussed based on the stability theory of fractional-order system, which may provide potential applications in secure communication. Finally, some numerical simulations are presented to show the effectiveness of the theoretical results.
Highlights
Though the concept of fractional calculus has been established more than three hundred years, its potential applications are fully carried out in recent decades, especially in the fields of control, engineering, and physics; see [1,2,3] and reference therein
The memristor, which was predicted as the missing circuit element [4], is more likely to be linked to fractional calculus due to its inherent features
The stability of fractional differential equation (FDE) is one of the most important aspects in FDE’s application of control process [5, 6], and Lyapunov stability method provides an efficient way to analyze the stability of FDE without explicitly solving the differential equations [7]
Summary
Though the concept of fractional calculus has been established more than three hundred years, its potential applications are fully carried out in recent decades, especially in the fields of control, engineering, and physics; see [1,2,3] and reference therein. In order to stabilize the chaotic FDE, many control mechanisms are presented so far, among which sliding mode control (SMC) technique is extensively adopted as it can be utilized to improve the control performance criteria such as the robustness and fast time response [8,9,10] Another important aspect of FDE’s application of control process lies in synchronization of fractional-order chaotic systems [11, 12], which attracts increasing attention in recent years due to its potential applications in secure communication.
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