Lag synchronisation of chaotic systems using sliding mode control

In this paper, lag synchronisation of chaotic systems with disturbances is investigated based on sliding mode control. The disturbance observer is developed to ensure the boundedness of the disturbance error dynamics by using the linear matrix inequality approach. Then by sliding mode control, a control scheme is designed to realise the lag synchronisation between a drive system and a response system with disturbances, and the sufficient condition of lag synchronisation is established. The Lyapunov stability theorem is used to verify that the error system can achieve an asymptotically stable condition. A specific chaotic system is taken as an example for numerical simulation demonstration to verify the effectiveness and feasibility of the proposed approach.