Sliding mode and LMI based control for fractional order unified chaotic systems

This paper investigates the chaos control problem for a class of fractional order unified chaotic systems. By introducing the sliding mode control method, a feedback controller is established to guarantee the asymptotical stability, and its parameter is obtained in terms of LMI, which can be easily obtained by Matlab's LMI Toolbox. A dynamic compensator is designed to overcome the difficulty of dealing with the nonlinear items in the chaotic system. To reduce the chattering phenomenon, a power reaching law is adopted. The validity of the methods is verified by a numerical example.