Small control property

In nonlinear control theory, a non-linear system of the form x ˙ = f ( x , u ) is said to satisfy the small control property if for every ε > 0 there exists a δ > 0 so that for all ∥ x ∥ < δ there exists a ∥ u ∥ < 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.