Robust control of networks under discrete disturbances and controls

We consider dynamic networks where the disturbances and control actions take discrete values. We briefly survey some of our recent results establishing necessary and sufficient conditions for the existence of robustly globally invariant (hyper box) sets, as well as sufficient conditions for global attractivity of such sets. We then establish connections between these results and existing results in the literature for the setup where all the inputs are analog. Finally, we derive tight upper and lower bounds on the smallest such set in the special case of a degenerate network