Control and Synchronization with Known and Unknown Parameters

In this paper, we consider the chaos control for 4D hyperchaotic system by two cases, known & unknown parameters based on Lyapunov stability theory via nonlinear control. We find that there are two cofactors that have an effect on determining any case to achieve the control, the two cofactors are proposed in the control and the matrix that produce from the time derivative of Lyapunov function. In adding, we find some weakness cases in Lyapunov stability theory. For this reason, we design with only one controller and perform a simple change in this control in order to recognize the difference between these cases although all of the controllers are almost similar.

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