Pinning consensus for multi-agent systems with non-linear dynamics and time-varying delay under directed switching topology

Yangling Wang; Jinde Cao; Jianqiang Hu

Pinning consensus for multi-agent systems with non-linear dynamics and time-varying delay under directed switching topology

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Author(s): Yangling Wang ^{1, 2} ; Jinde Cao ^{1, 3} ; Jianqiang Hu ⁴
- Affiliations: 1: Research Center for Complex Systems and Network Sciences, and Department of Mathematics, Southeast University, Nanjing 210096, People's Republic of China;
  2: School of Mathematics and Information Technology, Nanjing Xiaozhuang University, Nanjing 211171, People's Republic of China;
  3: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
  4: School of Automation, Southeast University, Nanjing 210096, People's Republic of China
Source: Volume 8, Issue 17, 20 November 2014, p. 1931 – 1939
DOI: 10.1049/iet-cta.2014.0032 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 08/01/2014, Accepted 31/07/2014, Revised 25/07/2014, Published 15/10/2014

This paper studies the leader-following consensus problem in directed networks of agents with non-linear dynamics and time-varying coupling delay by using the pinning control method. The main contribution of this study is that we obtain two classes of sufficient leader-following consensus criteria without assuming that the topology among followers is strongly connected or has a spanning tree, and without assuming that the derivative of the time-varying communication delay is less than 1. In addition, to be more practical we consider the general network whose coupling topology is arbitrarily switching among a finite set of topologies. Based on the common Lyapunov theory and linear matrix inequalities approach, we prove that the leader-following consensus problem can be solved only with the assumption that the topology among the followers has p (p > 1) and there is a directed path from the leader to each follower. Two examples are presented to show the applications of the criteria obtained in this study.

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Pinning consensus for multi-agent systems with non-linear dynamics and time-varying delay under directed switching topology

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