Large and small time local controllability

A control system is small time locally controllable, (STLC), along a rest solution p if for any t₁, α>0 all points in a neighborhood of p can be attained in time t₁ by use of measurable controls u having values |u(t)|⩽α. The system is large time locally controllable (LTLC) at p if for any α>0 there exists a t₁>0 such that all points in a neighborhood of p can be attained in time t₁ by controls satisfying |u(t)|⩽α. For smooth, affine systems, the authors give sufficient conditions for LTLC in terms of the local property, STLC, of an appropriate approximating system