Strong structural controllability under network perturbations
Shimaossadat Mousavi, ءMohammad Haeri, Mehran Mesbahi · Repository for Publications and Research Data (ETH Zurich) · 2019
This paper investigates the robustness of strong structural controllability for linear time-invariant and linear time-varying directed networks with respect to structural perturbations, including edge deletions and additions.In this direction, we introduce a new construct referred to as a perfect graph associated with a network with a given set of control nodes.The tight upper bounds on the number of edges that can be added to, or removed from a network, while ensuring strong structural controllability, are then derived.Moreover, we obtain a characterization of critical edge-sets, the maximal set of edges whose any subset can be respectively added to, or removed from a network, while preserving strong structural controllability.In addition, procedures for combining networks to obtain strongly structurally controllable network-of-networks are proposed.Finally, controllability conditions are proposed for networks whose edge weights, as well as their structures, can vary over time.