Study on the Global Property of the Smooth Chua's System

In this paper, we first give a constructive proof for the existence of globally exponential attractive set of Chua's system with a smooth nonlinear function. Then, we derive a series of simple algebraic sufficient conditions under which two same type of smooth Chua's systems are globally exponentially synchronized using simple linear feedback controls. Also, as the special cases of chaos synchronization, we consider global tracking and global exponentially tracking of periodic motions, as well as global stabilization and globally exponential stabilization of equilibrium points in smooth Chua's systems. We construct a series of simple, easily applicable feedback control laws. Computer simulation results are presented to verify the theoretical predictions.

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