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Necessary and Sufficient Conditions for Consensus of Delayed Fractional‐order Systems
Author(s) -
Shen Jun,
Cao Jinde
Publication year - 2012
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.492
Subject(s) - order (exchange) , stability (learning theory) , topology (electrical circuits) , domain (mathematical analysis) , network topology , mathematics , control theory (sociology) , consensus , fractional order system , fractional calculus , computer science , mathematical optimization , multi agent system , mathematical analysis , control (management) , combinatorics , finance , machine learning , artificial intelligence , economics , operating system
In this paper, we study the consensus problem of fractional‐order systems with input delays. Using L aplace transform method, the stability of the fractional‐order systems is first discussed in the frequency domain. Based on the generalized N yquist stability criterion, a necessary and sufficient condition is further derived to ensure the consensus of fractional‐order systems with identical input delays over directed interaction topology. Furthermore, when the interaction topology is undirected, the consensus condition of fractional‐order systems with heterogeneous input delays is explicitly given. Finally, some illustrative examples are presented to show the effectiveness and advantages of the theoretical results.