Abstract
This paper investigates a new wing doubled fractional-order chaos and its control. Firstly, a new fractional-order chaos is proposed, replacing linear termxin the second equation by its absolute value; a new improved system is got, which can make the wing of the original system doubled. Then, circuit diagram is presented for the proposed fractional-order chaos. Furthermore, based on fractional-order stability theory and T-S fuzzy model, a more practical stability condition for fuzzy control of the proposed fractional-order chaos is given assset of linear matrix inequality (LMI) and the strict mathematical norms of LMI are presented. Finally, numerical simulations are given to verify the effectiveness of the proposed theoretical results.
Highlights
Fractional calculus has the same history as integer calculus, which has appeared 300 years ago
People find that many actual systems can be well described with the help of fractional calculus, especially for memory and hereditary properties of various materials and processes [5,6,7]
In [22], by employing linear matrix inequality (LMI) method, a new fuzzy controller based on T-S fuzzy model is designed for chaos synchronization of two Rikitake generator systems
Summary
Fractional calculus has the same history as integer calculus, which has appeared 300 years ago. Chen et al proposed a new fractional-order chaotic system and the circuit synchronization of the system was implemented which was very important in theory and practice [15]. Linear matrix inequality (LMI), as a very important and classic tool, has been widely used in the fuzzy control and synchronization of integer-order chaos. In [22], by employing LMI method, a new fuzzy controller based on T-S fuzzy model is designed for chaos synchronization of two Rikitake generator systems. A new wing doubled fractional-order chaos is proposed and its experimental circuit simulation is presented. Based on fractionalorder stability theory, a more practical stability condition for fuzzy control of the proposed fractional-order chaos is proposed and the strict mathematical norms of LMI are presented.
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