We study the asymptotic properties of distributed consensus algorithms over switching directed random networks. More specifically, we focus on consensus algorithms over independent and identically distributed, directed random graphs, where each agent can communicate with any other agent with some exogenously specified probability. While different aspects of consensus algorithms over random switching networks have been widely studied, a complete characterization of the distribution of the asymptotic value for general \textit{asymmetric} random consensus algorithms remains an open problem. In this paper, we derive closed-form expressions for the mean and an upper bound for the variance of the asymptotic consensus value, when the underlying network evolves according to an i.i.d. \textit{directed} random graph process. We also provide numerical simulations that illustrate our results.
Designing Distributed Fixed-Time Consensus Protocols for Linear Multi-Agent Systems Over Directed Graphs
School of Automation, Northwestern Polytechnical University（西北工业大学自动化学院）；Department of Electronic Engineering, City University of Hong Kong（香港城市大学电子工程系）
Event-triggered consensus of multi-agent systems under directed topology based on periodic sampled-data
School of Mathematics and Statistics, Qingdao University（青岛大学数学与统计学院）；College of Automation and Electrical Engineering, Qingdao University（青岛大学自动化与电气工程学院）；School of Control Science and Engineering, Shandong University（山东大学控制科学与工程学院）
Non-trivial consensus on directed signed matrix-weighted networks with compound measurement noises and time-varying topologies
School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）；College of Computer Science and Software Engineering, Shenzhen University（深圳大学计算机科学与软件工程学院）
Grounded Laplacians of Directed Signed Matrix-Weighted Networks: Spectral Properties and Applications to Non-Trivial Consensus
the College of Computer Science and Software Engineering, Shenzhen University（深圳大学计算机科学与软件工程学院）；the School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）；the Faculty of Computer Science and Control Engineering, Shenzhen University of Advanced Technology（深圳先进技术大学计算机与控制工程学院）
