The paper introduces positive and negative signed zero forcing sets and shows that, when the sign pattern admits only real eigenvalues, a signed network is strongly structurally controllable if the control nodes form a signed, positive signed, and negative signed zero forcing set.
Strong Structural Controllability of Networks under Time-Invariant and Time-Varying Topological Perturbations
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abstract
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 sets 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.
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math.OC 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Strong Structural Controllability of Signed Networks
The paper introduces positive and negative signed zero forcing sets and shows that, when the sign pattern admits only real eigenvalues, a signed network is strongly structurally controllable if the control nodes form a signed, positive signed, and negative signed zero forcing set.