On finite-/fixed-time synchronization of multi-weighted dynamical networks: a new unified control approach

In this paper, a unified control strategy is proposed to explore the issues of finite-time (FTT) synchronization and fixed-time (FXT) one for multi-weighted dynamical networks (MWDNs) simultaneously. A new unified finite-/fixed-time (FTT/FXT) stability result is firstly derived for nonlinear dynamical systems, wherein the settling time is more precisely estimated. Then, by designing a novel feedback controller, unified sufficient conditions are established for FTT/FXT synchronization of the MWDNs under study. It is indicated that the conversion between FTT synchronization and FXT one can be realized through simply adjusting one control parameter, exhibiting the flexibility of the control scheme in real-world applications. Moreover, the designed unified control protocol does not contain signum function, which can avoid the occurrence of chattering phenomena during the synchronization process. In particular, a detailed analysis about the relationships between the settling time and the main control parameters is given, which facilitates the selection of control parameters in practice. Lastly, numerical simulations are presented to validate the correctness of the theoretical results.