Prescribed-Time Synchronization for Complex Networks With Additive Coupling

We discuss the prescribed-time synchronization for directed complex networks with additive coupling, where the settling time is independent of initial values and any other parameters. Considering the case that inner coupling matrices may be not available, we make full use of the irreducible and asymmetric outer coupling matrices and their normalized left eigenvectors (NLEVecs) corresponding to the zero eigenvalue to design a new vector by combining all these NLEVecs. We prove that if the Chebyshev distances between this vector and any NLEVec is in the region of allowable deviation for each matrix, then we can establish a new Lyapunov function with it to analyze the prescribed-time synchronization. Numerical simulations are provided to verify our theoretical results.