Fixed Time Synchronization of Complex Networks with Constant Time Delay

This paper investigates the fixed time synchronization (FxTSyn) problem for complex networks (CNs) with constant time delay. We design a useful controller composed of three terms, and using the so called two-phases method (2PM) in the literature of finite time (FnT) stability with delay, we prove that FxTSyn can be realized rigorously. In Phase I, synchronization (Syn) error is proved to decrease from any initial error values (IEV) to 1 in FxT; in Phase II, Syn error is proved to decrease from 1 to 0 in FxT, therefore, the whole time for Syn is fixed. Finally, a numerical example is given.