Dynamic sliding mode control of four dimensional hyperchaotic systems using LMI

The paper deals with the dynamic sliding mode control of four dimensional hyperchaotic systems. Only one control input has been used and moreover the controller is a simple sliding mode controller. Here it is shown that this simple control law suffices to stabilize the hyper-chaotic system to the zero equilibrium globally and asymptotically. Chattering has been successfully reduced by dynamic sliding surface and reaching law. The dynamic sliding surface is also used to improve the performance in sliding mode. The parameters of the sliding surface are obtained using linear matrix inequality (LMI). The simulation for hyperchaotic Xu and Qi system has been done using MATLAB.