Fixed/Preassigned-Time Synchronization Control of Complex Networks With Time Varying Delay

The problem of fixed-time (FXT) and preassigned-time (PAT) synchronization for delayed dynamic complex networks via developing control schemes is concerned. First, by comparing with the existing results, some new results for delayed networks model to ensure the synchronization of FXT and PAT are obtained. Second, some looser conditions are obtained for FXT synchronization, and several more accurate settling time (ST) estimates are established through several special functions. Third, by using some non-trivial control strategy, the PAT synchronization is investigated with limited control gains, and the synchronization time is able to specified in advance on the basis of practical need and is not relate to any parameter and any initial value. In particular, as a distinct form, the essential conditions for the FXT and PAT synchronization are obtained for the coupled neural networks. last, the improved the FXT and PAT synchronization results of dynamic delayed networks are demonstrated by one numerical example.