Synchronization of Complex Networks With Continuous or Discontinuous Controllers Based on New Fixed-Time Stability Theorem

Abstract

As the bounds of convergence time (CT) for fixed-time (FxT) stability have connections with some parameters of the system, the existing methods of FxT stability are still not really FxT. Therefore, this article studies FxT synchronization of complex networks (CNs) by proposing a new FxT stability theorem. First, the new FxT stability theorem is proposed, the CT of the system is any given time in advance, which is not concerning the starting value and parameters of the system. Second, a set of new controllers, including the continuous controller (CCr) and discontinuous controller (DCCr) are, respectively, designed to obtain the new FxT synchronization criteria for the CNs. Moreover, the control methods effectively solve the CT boundary problem associated with the system parameters in the previous FxT stability methods. Finally, numerical simulations and analog circuits are used to verify the effectiveness of the discussed method.