This article investigates a two-timescale opinion dynamics model, named the concatenated Friedkin–Johnsen (FJ) model, which describes the evolution of the opinions of a group of agents over a sequence of discussion events. The topology of the underlying graph changes with the event, in the sense that the agents can participate or less to an event, and the agents are stubborn, with stubbornness that can vary from one event to the other. Concatenation refers to the fact that the final opinions of an event become initial conditions of the next event. We show that a concatenated FJ model can be represented as a time-varying product of stochastic transition matrices having a special form. Conditions are investigated under which a concatenated FJ model can achieve consensus in spite of the stubbornness. Four different sufficient conditions are obtained, mainly based on the special topological structure of our stochastic matrices.  

　　Publication:  

　　IEEE Transactions on Automatic Control, Volume: 68, Issue: 7, July 2023.  

　　http://dx.doi.org/10.1109/TAC.2022.3200888  

　　Author:  

　　Lingfei Wang  

　　Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China  

　　University of Chinese Academy of Sciences, Beijing, China  

　　Carmela Bernardo  

　　Group for Research on Automatic Control Engineering, Department of Engineering, University of Sannio, Benevento, Italy  

　　Division of Automatic Control, Department of Electrical Engineering, Link？ping University, Link？ping, Sweden  

　　Yiguang Hong  

　　Department of Control Science and Engineering, Tongji University, Shanghai, China  

　　Email: yghong@iss.ac.cn  

　　Francesco Vasca  

　　Group for Research on Automatic Control Engineering, Department of Engineering, University of Sannio, Benevento, Italy  

　　Guodong Shi  

　　Australian Center for Field Robotics, School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, Australia  

　　Claudio Altafini  

　　Division of Automatic Control, Department of Electrical Engineering, Link？ping University, Link？ping, Sweden