New estimations for ultimate boundary and synchronization control for a disk dynamo system

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.