Observer-based control design for three well-known chaotic systems

In this paper, a singularity-free approach is proposed for controlling three well-known chaotic systems namely Lorenz, Chen and Lu. The control design guarantees the regulation of two states and boundedness of the remaining state. The stability of the proposed scheme has been shown using the Lyapunov stability theorem. Implementation of the proposed control technique requires system states, while in most of practical applications only the system output is available. To overcome this problem, a nonlinear observer is coupled with the controller. Simulation results have illustrated the effectiveness and robustness of the proposed schemes. If the control action is applied to the second system equation, all states will be regulated.