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r ‐consensus control for higher‐order multi‐agent systems with digraph
Author(s) -
Xin Youming,
Cheng Zunshui
Publication year - 2013
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.670
Subject(s) - digraph , order (exchange) , consensus , multi agent system , mathematics , discrete mathematics , combinatorics , control theory (sociology) , computer science , control (management) , artificial intelligence , economics , finance
This paper studies a consensus problem for l th ( l ≥ 2) order multi‐agent systems with digraph, namely, for a fixed r (0 ≤ r ≤ l − 1), the r th derivativex i rof the states x i of agents are convergent to a constant value and, for every k (0 ≤ k ≤ l − 1),x i k − x j kare convergent to zeros. A new concept of r ‐consensus is introduced and new consensus protocols are proposed for solving such an r ‐consensus problem. A sufficient and necessary condition for r ‐consensus is obtained. As special cases, criteria for third‐order systems are given, in which the exact relationship between feedback gains is established. Finally, an illustrative example is given to demonstrate the effectiveness of these protocols.