Analysis and discontinuous control for finite-time synchronization of delayed complex dynamical networks

This paper addresses the finite-time and fixed-time synchronization issue of delayed complex dynamical networks (CDNs). Firstly, as an important preliminary, an improved and generalized finite-time stability theory is established for delayed nonlinear systems to prove the finite-time synchronization mainly through the reduction to absurdity. Different from some existing results, a more detailed discussion of the setting time function for finite-time synchronization is given. Besides, a novel feedback controller is firstly proposed to unify finite-time and fixed-time synchronization just by adjusting the key control parameter. Furthermore, several new criteria are derived to ensure the finite-time and fixed-time synchronization based on inequality analysis method and constructing appropriate Lyapunov functional. Finally, some numerical simulations are presented to support the theoretical results.