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Linear feedback control, adaptive feedback control and their combination for chaos (lag) synchronization of LC chaotic systems. (English) Zbl 1136.93430
Summary: We study chaos (lag) synchronization of a new LC chaotic system, which can exhibit not only a two-scroll attractor but also two double-scroll attractors for different parameter values, via three types of state feedback controls: (i) linear feedback control; (ii) adaptive feedback control; and (iii) a combination of linear feedback and adaptive feedback controls. As a consequence, ten families of new feedback control laws are designed to obtain global chaos lag synchronization for $\tau <0$ and global chaos synchronization for $\tau =0$ of the LC system. Numerical simulations are used to illustrate these theoretical results. Each family of these obtained feedback control laws, including two linear (adaptive) functions or one linear function and one adaptive function, is added to two equations of the LC system. This is simpler than the known synchronization controllers, which apply controllers to all equations of the LC system. Moreover, based on the obtained results of the LC system, we also derive the control laws for chaos (lag) synchronization of another new type of chaotic system.
##### MSC:
 93D15 Stabilization of systems by feedback 34D99 Stability theory of ODE 93B52 Feedback control 93C40 Adaptive control systems 37D45 Strange attractors, chaotic dynamics