Globally exponentially attractive set and synchronization controlling of a new chaotic system

In the paper, we firstly investigate the globally exponentially attractive set of a new chaotic system via the generalized Lyapunov function theory and a concrete spheroid estimation of the globally exponentially attractive set of the chaotic system was obtained without existence assumptions. Secondly, based on some inequalities techniques, linear feedback control with one state feedback and one input or two inputs is proposed to realize the globally exponential synchronization of two identical chaotic systems. Some sufficient algebraic criteria for the globally exponential synchronization are obtained analytically. The control performances are verified by numerical simulations.