If a linearization is controllable, is the full nonlinear case always controllable also? Does this apply for any initial conditions or only a limited region?

Shreesh P. Mysore, Oct 28 02

Yes. The full nonlinear system is controllable in a small neighborhood of the eqm. point, if the linearization about the eqm point is controllable. Note that this can be proved only for a \textit{small nbhd}. (See Prop 11.2, p.511 in "Nonlinear systems" by Shankar Sastry for proof.)