Finite-Time Lag Synchronization of Uncertain Complex Dynamical Networks With Disturbances via Sliding Mode Control

This paper investigates lag synchronization between two uncertain complex dynamical network with time-varying coupling delay, fully unknown parameters, and disturbances in finite-time. First, a nonsingular terminal sliding surface is proposed and its finite convergence is proved. Then, appropriate adaptive laws are derived to estimate the unknown parameters of the networks. Subsequently, based on the finite-time stability theory and adaptive laws, an adaptive sliding mode control is designed for achieving finite-time lag synchronization. In addition, the unknown bounded disturbances are also overcame by the proposed control and some corollaries are given. Finally, analytical results show that the states trajectory of the networks error converge to the sliding phase within finite-time. Furthermore, numerical simulation results demonstrate the applicability and the effectiveness of the designed method.