Relaxed conditions for norm-controllability of nonlinear systems

In this paper, we further study the recently introduced notion of norm-controllability, which captures the responsiveness of a nonlinear system with respect to applied inputs in terms of the norm of an output map. We give sufficient conditions for this property based on higher-order lower directional derivatives, which generalize the results obtained in our earlier work and help to establish norm-controllability for systems with outputs having relative degree greater than one. Furthermore, we illustrate the obtained results by means of a chemical reaction example.