TABLE OF CONTENTS Let V be a neighborhood of a point 
(i.e., an n-dimensional open set of 
containing x). Let R V ( x, T) indicate the set of reachable points at time T by trajectories remaining inside V and satisfying equation (12.6), and let
We define the following four versions of nonlinear controllability (see figure 12.11):
The system is controllable from x if, for any 
, there exists a T > 0 such that 
. In other words, any goal state is reachable from x in finite time.
The system is accessible from x if 
contains a full n-dimensional subset of 
for some T > 0. See figure 12.11(a).
The system is small-time locally accessible ( STLA) from x if R V ( x, ? T) contains a full n-dimensional subset of 
for all neighborhoods V and all T > 0. See figure 12.11(b).
The system is small-time locally controllable ( STLC) from x if R V ( x, ? T) contains a neighborhood of x for all neighborhoods V and all T > 0. See figure 12.11(c).
. (a) This system is accessible from x, but neither small-time locally accessible (STLA) nor small-time locally controllable (STLC). The reachable set is two-dimensional, but...
