Controllability of Networks of Linear Systems: a Graph Theoretic Approach
Seyed Sina Jahadihosseini · TSpace (University of Toronto) · 2018
In this thesis, we study the controllability of networked single-input single-output linear time-invariant systems. We show that necessary conditions for the controllability of networks of single-integrators such as dilation, input-symmetry and equitable partitioning do not apply, in general, to more complex networks. We introduce new necessary and sufficient conditions for the controllability of networks in terms of the interconnection topology and sub-systems' properties. We also provide a number of graph-theoretic necessary conditions for controllability of networks. As a particular case of our results, we will provide necessary conditions for the controllability of diffusively coupled networks. Finally, we illustrate our results by studying the controllability of a simple neuronal network model.