Clock synchronization over directed graphs

One of the requirements for distributed control and estimation applications in wireless networks is that all nodes have a common timescale. Recently, a clock synchronization method has been proposed which is based on a model consisting of heterogeneous double-integrators and distributed linear update rules. In this paper, we extend these results to networks with directed communication topology. We provide necessary and sufficient conditions under which synchronization is guaranteed over directed graphs and present an easy-to-check graphical stability condition for analysis and design purposes. Furthermore, we characterize the resulting common clock speed of the synchronized network. Various numerical examples illustrate the results.