  In this note, we study the prescribed-time (PT) synchronization of
multiweighted and directed complex networks (MWDCNs) via pinning control.
Unlike finite-time and fixed-time synchronization, the time for synchronization
can be preset as needed, which is independent of initial values and parameters
like coupling strength. First and foremost, we reveal the essence of PT
stability by improper integral, L'Hospital rule and Taylor expansion theory.
Many controllers established previously for PT stability can be included in our
new model. Then, we apply this new result on MWDCNs as an application. The
synchronization error at the prescribed time is discussed carefully, so, PT
synchronization can be reached. The network topology can be directed and
disconnected, which means that the outer coupling matrices (OCMs) can be
asymmetric and not connected. The relationships between nodes are allowed to be
cooperative or competitive, so elements in OCMs and inner coupling matrices
(ICMs) can be positive or negative. We use the rearranging variables' order
technique to combine ICMs and OCMs together to get the sum matrices, which can
make a bridge between multiweighted and single-weighted networks. Finally,
simulations are presented to illustrate the effectiveness of our theory.
