Conditions for Feedback Linearization of Network Systems

Feedback linearization allows for the local transformation of a nonlinear system to an equivalent linear one by means of a coordinate transformation and a feedback law. Feedback linearization of large-scale nonlinear network systems is typically difficult, since existing conditions become harder to check as the network size becomes larger. In this letter, we provide novel conditions to test whether a nonlinear network is feedback-linearizable. Specifically, given some dedicated control inputs injected to a set of network nodes, we derive an easy-to-check algebraic condition that can be tested on the Jacobian matrix of the network dynamics evaluated at some desired working point. Furthermore, our requirements are sufficient for (local) controllability, and thus provide a testable condition for controllability of large-scale nonlinear networks. Finally, we validate our findings by enforcing the formation of desired synchronization patterns in networks of coupled oscillators.