Open AccessMulti-leader-follower group consensus of stochastic time-delay multi-agent systems subject to Markov switching topology
Author(s) -
Tao Guo,
Jing Han,
Cancan Zhou,
Jianping Zhou
Publication year - 2022
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2022353
Subject(s) - multi agent system , markov chain , convex combination , convex hull , mathematics , control theory (sociology) , model transformation , mathematical optimization , topology (electrical circuits) , protocol (science) , group (periodic table) , transformation (genetics) , regular polygon , graph , computer science , markov process , lyapunov function , control (management) , convex optimization , discrete mathematics , combinatorics , nonlinear system , alternative medicine , consistency (knowledge bases) , artificial intelligence , chemistry , pathology , biochemistry , geometry , quantum mechanics , medicine , statistics , physics , organic chemistry , gene
The multi-leader-follower group consensus issue of a class of stochastic time-delay multi-agent systems subject to Markov switching topology is investigated. The purpose is to determine a distributed control protocol to make sure that the followers' states converge in mean square to a convex hull generated by the leaders' states. Through a model transformation, the problem is transformed into a mean-square stability issue of a new system. Then, an easy-to-check sufficient condition for the solvability of the multi-leader-follower group consensus issue is proposed by utilizing the Lyapunov stability theory, graph theory, as well as several inequality techniques. It is shown that the required feedback gain can be acquired once the condition is satisfied. Finally, an example is used to illustrate the effectiveness of the control protocol.