Finite-time lag synchronization of time-varying delayed complex networks via periodically intermittent control and sliding mode control

In this paper, finite-time lag synchronization of time-varying delayed complex networks is investigated. By designing a periodically intermittent feedback controller and adjusting periodically intermittent control strengths with the updated laws in two parts respectively, we achieve finite-time lag synchronization between two time-varying delayed complex networks. In addition, based on the same finite-time stability theory and the same sliding mode control, we ensure that the trajectory of error system converges to a chosen sliding surface within finite time and remains on it forever. Finally, two examples are given to demonstrate the effectiveness and correctness of the theoretical results obtained here. •The lag synchronization relies on two periodically intermittent controllers.•The error trajectory converges to a chosen sliding surface.•The finite-time stability theory is used to prove the stability.•Convergence in time is given by the finite-time stability theory.