Abstract
Synchronization is an essential feature for the use of digital systems in
telecommunication networks, integrated circuits, and manufacturing automation.
Formerly, master-slave (MS) architectures, with precise master
clock generators sending signals to phase-locked loops (PLLs) working as
slave oscillators, were considered the best solution. Nowadays, the development
of wireless networks with dynamical connectivity and the increase
of the size and the operation frequency of integrated circuits suggest that
the distribution of clock signals could be more efficient if distributed solutions
with fully connected oscillators are used. Here, fully connected
networks with second-order PLLs as nodes are considered. In previous
work, how the synchronous state frequency for this type of network depends
on the node parameters and delays was studied and an expression
for the long-term frequency was derived (Piqueira, 2006). Here, by taking the first term
of the Taylor series expansion for the dynamical system description, it is
shown that for a generic network with N nodes, the synchronous state is
locally asymptotically stable.