Predefined-Time Robust Synchronization for Complex Networks with External Disturbance via Sliding Mode Control

This paper is concerned with the predefined-time synchronization problem for complex networks in the presence of parameter uncertainty and external disturbance, where the nonlinear function involved is general that satisfies the sector-bounded constraint instead of the usual Lipschitz condition adopted. Firstly, an integral sliding mode surface is constructed, by using the predefined-time stability criterion and the Kronecker product, sufficient conditions in the form of linear matrix inequalities are derived to guarantee the predefined-time stability of the synchronization error system during the sliding mode phase. Then, the sliding mode control law is explicitly designed such that the error system can be driven onto the specified sliding mode surface within the predefined-time. Finally, a numerical example is presented to illustrate feasibility of the obtained results.