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