Hansen's problem

A non-linear system of the form $\dot{x}=f(x,u)$ is said to satisfy the small control property if for every $ϵ>0$ there exists a $\delta >0$ so that for all $\left|\right|x\left|\right|<\delta$ there exists a $\left|\right|u\left|\right|<ϵ$ so that the time derivative of the system's Lyapunov function is negative definite at that point.

In other words, even if the control input is arbitrarily small, a starting configuration close enough to the origin of the system can be found that is asymptotically stabilizable by such an input.