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This paper investigates the impact of addition/removal of edges in a complexnetworked control system, for the purposes of improving its controllability,system performances or robustness to external disturbances. The transferfunction formulation we obtain allows to quantify the impact of an edgemodification with the $\hinf$ and $\htwo$ norms. For stable networks withpositive edge weights, we show that the $\hinf$ norm can be computed exactlyfor each possible single edge modification, as well as the associated stabilitymargin. For the $\htwo$ norm we instead obtain a lower bound. Since this boundis linked to the trace of the controllability Gramian, it can be used forinstance to reduce the energy needed for control. When instead the dynamics isof Laplacian type, then the norms become unbounded. However, the associateddisplacement systems are stable and for them the effect of edge modificationscan be quantified. In particular, in this case we provide an upper bound on the$ \hinf$ norm and compute the exact value of the $ \htwo $ norm for arbitraryedge additions.

Investigating the effect of edge modifications on networked control systems