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Laplacian dynamics on cographs: controllability analysis through joins and unions

Mousavi, S. S ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.1109/TAC.2020.2992444
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2021
  4. Abstract:
  5. In this article, we examine the controllability of Laplacian dynamic networks on cographs. Cographs appear in modeling a wide range of networks and include as special instances, the threshold graphs. In this article, we present necessary and sufficient conditions for the controllability of cographs, and provide an efficient method for selecting a minimal set of input nodes from which the network is controllable. In particular, we define a sibling partition in a cograph and show that the network is controllable if all nodes of any cell of this partition except one are chosen as control nodes. The key ingredient for such characterizations is the intricate connection between the modularity of cographs and their modal properties. Finally, we use these results to characterize the controllability conditions for certain subclasses of cographs. © 1963-2012 IEEE
  6. Keywords:
  7. Controllability ; Laplace transforms ; Control nodes ; Controllability analysis ; Controllability condition ; Dynamic network ; Input node ; Laplacians ; Modal properties ; Threshold graphs ; Graph theory
  8. Source: IEEE Transactions on Automatic Control ; Volume 66, Issue 3 , 2021 , Pages 1383-1390 ; 00189286 (ISSN)
  9. URL: https://ieeexplore.ieee.org/document/9086131