Generic Controllability of Networks With Identical SISO Dynamical Nodes

Recently, controllability of linear systems has been studied for various applications in large networks in biology, physics, and engineering. To address scale and lack of precise knowledge of the network parameters issues, tools from structured system theory are well indicated for such study. Precisely, generic properties, i.e., properties that are true for almost all values of the parameters, can be stated. While most existing results concern networks of single integrators, in this article, we show that generic controllability of a network of identical single-input-single-output controllable and observable systems is ensured if and only if the structural controllability conditions are satisfied for the graph representing the network. This result constitutes an important generalization of the famous Lin's theorem stated in the 1970s. It is even the broadest generalization of this theorem.