Title: Comments on 'Controllability analysis of multi-agent systems using relaxed equitable partitions'

Authors: M.K. Camlibel; S. Zhang; M. Cao

Addresses: Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, NL-9700 AK Groningen, The Netherlands; Department of Electronics and Communication Engineering, Dogus University, Acibadem 34722, Istanbul, Turkey. ' University of Groningen, Research Institute of Industrial Technology and Management, Nijenborgh 4, NL-9747 AG Groningen, The Netherlands. ' University of Groningen, Research Institute of Industrial Technology and Management, Nijenborgh 4, NL-9747 AG Groningen, The Netherlands

Abstract: We want to comment on a recent paper by Martini et al. [see Int. J. Systems, Control and Communication, Vol. 2, Nos. 1-3, pp.100-121, 2010]. The above paper analyses controllability of a class of multi-agent systems using the leader-invariant relaxed equitable partition (LEP) of their underlying graphs. Two of its main results rely on the complete characterisation of the controllable subspace of the system in terms of the characteristic vectors obtained from the LEP. By providing counterexamples for these results, this note shows that LEP cannot fully characterise the controllable subspace. Therefore, finding graphical necessary and sufficient conditions for controllability of this class of systems is still an open problem.

Keywords: multi-agent systems; MAS; agent-based systems; controllability; leader-invariant relaxed equitable partition; controllable subspace.

DOI: 10.1504/IJSCC.2012.045932

International Journal of Systems, Control and Communications, 2012 Vol.4 No.1/2, pp.72 - 75

Available online: 19 Mar 2012 *

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