LAUSR

Finite-time synchronization (FTS) of dynamical networks has received much attention in recent years, as it has fast convergence rate and good robustness. Most existing results rely heavily on some global condition such as the Lipschitz condition, which has limitations in describing the strong nonlinearity of most real systems. Dealing with strong nonlinearity in the field of FTS is still a challenging problem. In this article, the FTS problem of impulsive dynamical networks with general nonlinearity (especially strong nonlinearity) is considered. In virtue of the concept of nonlinearity strength that quantizes the network nonlinearity, local FTS criteria are established, where the range of the admissible initial values and the settling time are solved. For the networks with weak nonlinearity, global FTS criteria that unify synchronizing, inactive, and desynchronizing impulses are derived. Differing from most existing studies on FTS, the node system here does not have to satisfy the global Lipschitz condition, therefore covering more situations that are practical. Finally, numerical examples are provided to demonstrate our theoretical results.