Analysis of an averaging based synchronization algorithm in continuous-time

Abstract

Synchronization in distributed networks plays a significant role in a broad range of applications that consist of mobile and/or wireless nodes which need to agree on a common notion of time to successfully fulfill the tasks that they are designed for. In this thesis, we introduce an averaging based distributed synchronization algorithm in continuous time and investigate its convergence properties for networks with time varying topology and time delay. The proposed distributed synchronization scheme is advantageous in the sense that it can be applied to large-scale networks due to its energy efficiency and its robustness to node failures. In the study of convergence properties, we utilize related results from graph theory, tools of Lyapunov functions, and Laplace transform. For fixed and time varying topology networks, it is shown that average consensus is achieved in the presence of free running frequencies, if the network is strongly connected and balanced. The result is also extended to networks with equal time delay, if the network topology is fixed, undirected, and connected. Extensive simulation results are carried out in Matlab to examine the related convergence scenarios.