Strong Structural Controllability of Networks under Time-Invariant and Time-Varying Topological Perturbations

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