Chaos control and global synchronization of Liu chaotic systems using linear balanced feedback control

Liu chaotic systems exhibit two- or four-scroll attractors and are observed in a variety of engineering phenomena, including rigid body motion, brushless DC motor system and so forth. This study applies the Lyapunov stability theorem to identify the sufficient conditions for the asymptotic stability of the equilibrium points of Liu chaotic systems. A linear balanced feedback gain control method is then employed to design a controller to achieve the global synchronization of two identical four-scroll Liu chaotic systems. The feasibility and effectiveness of the proposed chaos stability and synchronization schemes are verified via numerical simulations.