New estimations for ultimate boundary and synchronization control for a disk dynamo system |
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| Institution: | 1. Departamento de Control Automático, CINVESTAV-IPN, Av. IPN 2508, Col. San Pedro Zacatenco, 07360 D.F., Mexico;2. Universidad Politécnica de Tlaxcala Av., Universidad Politécnica de Tlaxcala No. 1 San Pedro Xalcaltzinco, Tepeyanco Tlaxcala, C.P. 90180, Mexico;1. LAMIS Laboratory, Department of Mathematics and Computer Science, University of Tebessa, Algeria;2. School of Basic Sciences and Humanities, German Jordanian University, Amman 11180, Jordan;3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;4. Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan;1. Department of Mechanics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China;2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China;3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, PR China |
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| Abstract: | We consider globally exponentially attractive sets and synchronization control for a disk dynamo system. First, based on generalized Lyapunov function theory and the extremum principle of function, we derive some new 4D ellipsoid estimations and a polydisk domain estimation of the globally exponentially attractive set of a 4D disk dynamo system without existence assumptions. Our results improve existing results on the globally exponentially attractive set as special cases and can lead to a series of new estimations. Second, we propose linear feedback control with a single input or two inputs to realize globally exponential synchronization of two 4D disk dynamo systems using inequality techniques. Some new sufficient algebraic criteria for the globally exponential synchronization of two 4D disk dynamo systems are obtained analytically. The controllers designed here have a simple structure and less conservation. Finally, numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme. |
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| Keywords: | Disk dynamo system Globally exponentially attractive set Generalized Lyapunov function Globally exponential synchronization Linear feedback Inequality |
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