On controllability of positive nonlinear continuous-time systems

Various controllability properties of positive nonlinear continuous-time systems are studied. It is shown that positive reachability is possible only from the origin, similarly as for linear systems. Also null controllability in finite time from any nonzero state is not possible. On the other hand nonlinear systems allow for less restrictive conditions for asymptotic null controllability than linear systems, for which this property is equivalent to asymptotic stability. It is shown that a nonlinear system is asymptotically null controllable if the basin of attraction of the system contains a curve that lies in the interior of the positive cone and one can steer from the initial point to the basin of attraction.