On control of networks of dynamical systems

We consider a network of dynamical systems whose trajectories we wish to control by applying stimuli to a subset of systems. We study the minimum number of systems to control and which systems to control and provide sufficient conditions and necessary conditions for successful control. These conditions are given in terms of graph theoretical properties of the underlying network. For instance, we show that for the cycle graph, the best way to achieve control is by applying control to systems that are approximately equally spaced apart.