Small control property

For applied mathematics, in nonlinear control theory, a non-linear system of the form $$\dot{x} = f(x,u)$$ is said to satisfy the small control property if for every $$\varepsilon > 0$$ there exists a $$\delta > 0$$ so that for all $$\|x\| < \delta$$ there exists a $$\|u\| < \varepsilon$$ 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.