Fixed-time sliding mode controller design for synchronization of complex dynamical networks

This paper investigates the fixed-time synchronization of complex dynamical networks with nonidentical nodes in the presence of bounded uncertainties and disturbances using sliding mode control technique. Firstly, a novel sliding surface is introduced and fixed-time stability of the sliding mode dynamics is proven by benefiting from Gudermannian function. Then, a novel sliding mode controller is proposed whereby fixed-time stability of the reaching mode is guaranteed. The outstanding feature of the proposed controller is that fixed convergence times of reaching and sliding modes are independent design parameters explicitly existing in the control law. This allows us not only to set the reaching time of reaching mode and settling time of sliding mode at any desired values in advance but also to adjust them independent of each other and in the most straightforward possible way. Finally, simulation results are reported in order to show the effectiveness of the proposed controller.