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

  • Authors:

  • M. K. Camlibel;S. Zhang;M. Cao

  • Affiliations:

  • 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 Engineeri ...;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

  • Venue:
  • International Journal of Systems, Control and Communications
  • Year:
  • 2012

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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.