Synchronization performance for arbitrarily connected network architectures

Phase-locked master slave (MS), mutual synchronous (MUS) and hierarchical synchronization networks are considered. The steady-state frequencies of a connecting synchronization network are investigated and shown to be functions of the network architecture, the network connection matrix, the network transmission delay matrix and the intrinsic frequencies of the nodal clocks/oscillators. Explicit expressions for the steady-state frequencies of the master and slave clocks are presented along with upper and lower bounds on these frequencies. Several theorems are provided which give considerable insight into the problem of investigating and establishing the performance of a connecting sync network in which nodes are added or deleted as the network deployment evolves. In particular, it is shown in an equation that the sync information is (1) power coupled from the master group of nodes to the slave group of nodes and then (2) power coupled among nodes in the slave group. The other two theorems are useful in predicting network performance when nodes are added or deleted from the network, i.e., as the network evolves