A New Fixed Time Synchronization Scheme for the Perturbed Complex Networks via Sliding Mode Control

ABSTRACT The research on fixed‐time synchronization (FTSyn) for complex networks with non‐identical nodes and disturbances is considered by using a sliding mode approach. First, a new and more general fixed‐time stability theorem (FTST) is put forward via an integral inequality technique, where the convergence time can be easily estimated by a simple formula regardless of initial conditions. Then, considering the effect of disturbances, a novel robust control strategy for the fixed‐time synchronization of complex networks is proposed by introducing a new sliding mode manifold. In our control framework, the controlled error system has immunity to the external disturbances, and the synchronization time can be flexibly adjusted by the control parameters, and its upper bound can be worked out by a simple calculation formula. Finally, an actual complex network composed of some classic chaotic systems is employed to perform numerical simulations, illustrating the effectiveness of the obtained results.