Abstract
In this paper, two kinds of chaotic systems are controlled respectively with and without time-delay to eliminate their chaotic behaviors. First of all, according to the first-order approximation method and the stabilization condition of the linear system, one linear feedback controller is structured to control the chaotic system without time-delay, its chaotic behavior is eliminated and stabilized to its equilibrium. After that, based on the first-order approximation method, the Lyapunov stability theorem, and the matrix inequality theory, the other linear feedback controller is structured to control the chaotic system with time-delay and make it stabilized at its equilibrium. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the two linear feedback controllers.
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