Laplacian Dynamics on Cographs: Controllability Analysis through Joins and Unions
22 May 2020
•
Mousavi Shima Sadat
•
Haeri Mohammad
•
Mesbahi Mehran
In this paper, 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 work, 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.(read more)