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Discrete‐time global leader‐following consensus of a group of general linear systems using bounded controls
Author(s) -
Zhao Zhiyun,
Lin Zongli
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.3749
Subject(s) - bounded function , adjacency matrix , multi agent system , eigenvalues and eigenvectors , strongly connected component , directed graph , relay , topology (electrical circuits) , graph , computer science , network topology , mathematics , unit circle , discrete time and continuous time , control theory (sociology) , control (management) , discrete mathematics , combinatorics , computer network , mathematical analysis , power (physics) , physics , statistics , quantum mechanics , artificial intelligence
Summary This paper deals with the problem of global leader‐following consensus of a group of discrete‐time general linear systems with bounded controls. For each follower agent in the group, we construct both a bounded state feedback control law and a bounded output feedback control law. The feedback laws for each input of an agent use a multi‐hop relay protocol, in which the agent obtains the information of other agents through multi‐hop paths in the communication network. The number of hops each agent uses to obtain its information about other agents for an input is less than or equal to the sum of the number of real eigenvalues on the unit circle and the number of pairs of complex eigenvalues on the unit circle of the subsystem corresponding to the input, and the feedback gains are constructed from the adjacency matrix of the communication network. We show that these control laws achieve global leader‐following consensus when the communication topology among follower agents forms a strongly connected and detailed balanced directed graph and the leader is a neighbor of at least one follower agent. Copyright © 2017 John Wiley & Sons, Ltd.