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Consensus of second‐order discrete‐time multi‐agent systems with relative‐state‐dependent noises
Author(s) -
Wang Bo,
Tian YuPing
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3816
Subject(s) - digraph , consensus , laplacian matrix , strongly connected component , sequence (biology) , network topology , discrete time and continuous time , mathematics , topology (electrical circuits) , eigenvalues and eigenvectors , multi agent system , state (computer science) , dwell time , directed graph , order (exchange) , computer science , control theory (sociology) , laplace operator , combinatorics , control (management) , algorithm , mathematical analysis , artificial intelligence , biology , genetics , operating system , quantum mechanics , medicine , clinical psychology , statistics , physics , finance , economics
Summary This paper studies the consensus problem of second‐order discrete‐time multi‐agent systems with relative‐state‐dependent noises. Directed switching topologies are considered. Firstly, for a kind of switching topology with each digraph containing a spanning tree, we give a weak consensus result on the basis of the mode‐dependent average dwell time method. Then, if all digraphs in a switching topology are strongly connected and the corresponding Laplacian matrices have a common left eigenvector for zero eigenvalue, we prove that the mean square and almost sure consensus can always be guaranteed for an arbitrary switching sequence with some constant distributed control gains, and we also give the statistic properties of the final consensus points. Numerical examples are presented to illustrate the effectiveness of our results. Copyright © 2017 John Wiley & Sons, Ltd.