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