Deterministic Synchronization Algorithms and Convergence Rates

In this paper, we study distributed deterministic algorithms to be used for synchronization in networks whose topologies may be time-varying. The problem is formulated as products of row-stochastic matrices which is a well-studied area in the mathematics literature. We derive the general conditions for synchronization and the existence of a common norm for an expanded set of row-stochastic matrices. This relation helps us understand why synchronization can be achieved by averaging the received data when there exist nodes that share information with others in the network. We then extend our results to time-varying and interval matrices, and study the convergence rates