Abstract:
There are numerous network applications where nodes require a common notion of time, and as such distributed synchronization is an important task in topology varying networks. In this thesis, we introduce a well known averaging based distributed synchronization algorithm and investigate its convergence conditions under varying topologies and delay. When data are transmitted through the network, communication delays are un- avoidable and it might degrade system performance. Furthermore, delay can cause a stable system go unstable unless certain conditions are met. In this thesis, the conver- gence of the consensus algorithm for delay varying networks is studied using properties of scrambling matrices. It is shown that delay does not affect the convergence of the algorithm so long as it is bounded. The effect of delay on convergence speed for some well known topologies is also discussed. In order to reduce convergence time, fastest converging system matrices are found for networks with symmetric connections by us- ing Linear Matrix Inequalities. It is also shown that the fastest converging matrices for fixed topologies will not provide the fastest convergence for varying topology networks. Consensus algorithms are investigated for networks not only with non–faulty nodes, but also with the faulty ones (or Byzantine nodes) that try to obstruct syn- chronization by sending wrong clock information to other nodes. It is shown that a network with Byzantine nodes will not be synchronized if the network topology and synchronization algorithm do not meet some conditions. Theoretical results are also illustrated by numerical examples.
