On norm-controllability of nonlinear systems

In this paper, we introduce and study the notion of “norm-controllability” for nonlinear systems. This property captures the responsiveness of a system with respect to the applied inputs, which is quantified via the norm of an output map. As a main contribution, we obtain a Lyapunov-like sufficient condition for norm-controllability. Several examples illustrate the various aspects of the proposed concept, and we also further elaborate norm-controllability for the special case of linear systems.