Stabilization and destabilization of network processes by sparse remote feedback: Graph-theoretic approach

The control of dynamical processes in networks is considered, in the case where measurement and actuation capabilities are sparse and possibly remote. Specifically, we study control of a canonical network dynamics, when only one network component´s state can be measured and only one (in general different) component can be actuated. To do so, we characterize the finite- and infinite- zeros of the resulting SISO system in terms of the graph topology. Using these results, we establish graphical conditions under which a network dynamics is stable/unstable upon application of any static linear feedback. We also give graphical conditions for destabilization of a stable network´s dynamics with high-gain static feedback. These conditions depend on the length, strength, and number of the paths from the component where the input is applied to the component where the measurements are made.