On Russell's method of controllability via stabilizability (Q1072499)

\textit{D. L. Russell} [Lect. Notes Pure Appl. Math. 43 (1979; Zbl 0408.93002)] has observed that a linear system is controllable provided it is stabilizable in both positive and negative time. We give a version of this result valid for nonlinear systems, and illustrate its use by giving new proofs of two classical results from control theory, the first involving bounded perturbations of controllable linear systems, and the second involving controllability of linear systems by bounded controls.