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Abstract
In this paper, we address the containment control problem for multi-agent systems under heterogeneous unbounded communication delays with emphasis on the convergence rate analysis. Different from most works on multi-agent systems, we resort to a viewpoint from the area of positive delay systems. We first cast the containment control problem into the stability analysis of an associated error system. In order to capture the convergence rate, we introduce a nondecreasing positive function whose reciprocal represents the decay rate of the associated error system. Under the assumption that each follower has access to at least one leader and some mild hypotheses on the communication delays, an explicit condition is given to characterise the decay rate of the associated error system in terms of linear programming. In addition, we provide several special cases when the communication delays are restricted by linear, sublinear and logarithmic growth rates, respectively. Finally, through numerical examples, it is shown that the convergence rate is dominated by the delays being the highest order infinitely large quantity.
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Notes on contributors
Jun Shen
Jun Shen received his BSc and MSc degrees from Southeast University, Nanjing, China, in 2008 and 2011, respectively. He is currently working toward his PhD degree with the Department of Mechanical Engineering, the University of Hong Kong, Hong Kong. He was a recipient of the Outstanding Master Degree Thesis Award from Jiangsu Province, China, in 2012. His current research interests include fractional order systems, positive systems, model reduction, robust control and filtering, and complex networks.
James Lam
James Lam received his BSc (first-class honours) degree in mechanical engineering from the University of Manchester, and was awarded the Ashbury Scholarship, the A.H. Gibson Prize, and the H. Wright Baker Prize for his academic performance. He obtained his MPhil and PhD degrees from the University of Cambridge. His doctoral and post-doctoral research projects were supported by the Croucher Foundation Scholarship and Fellowship. He was a recipient of the Outstanding Researcher Award of the University of Hong Kong and a Distinguished Visiting Fellow of the Royal Academy of Engineering. Prior to joining the University of Hong Kong in 1993, he held lectureships at the City University of Hong Kong and the University of Melbourne. He is a chartered mathematician, chartered scientist, chartered engineer, fellow of the Institute of Electrical and Electronic Engineers, fellow of the Institution of Engineering and Technology, fellow of the Institute of Mathematics and Its Applications, and fellow of the Institution of Mechanical Engineers. He is editor-in-chief of the IET Control Theory and Applications, subject editor of the Journal of Sound and Vibration, associate editor of Automatica, Asian Journal of Control, International Journal of Systems Science, International Journal of Applied Mathematics and Computer Science, Journal of the Franklin Institute, Multidimensional Systems and Signal Processing, and Proc. IMechE Part I: Journal of Systems and Control Engineering. He is also a member of the IFAC Technical Committee on Networked Systems. He was an associate editor of the IEEE Transactions on Signal Processing and a member of the IFAC Technical Committee on Control Design. He has also served the Engineering Panel of the Research Grants Council, HKSAR. Professor Lam has research interests in model reduction, robust control and filtering, delay, singular systems, Markovian jump systems, multidimensional systems, networked control systems, vibration control, and biological networks. He is a co-recipient of the International Journal of Systems Science Prize Paper Award.