Now suppose that a system is given on a smooth manifold as defined throughout Chapter 13 and used extensively in Chapter 14. The system can be considered as a parameterized family of vector fields in which is the parameter. For stability, it was assumed that this parameter was fixed by a feedback plan to obtain some . This section addresses controllability, which indicates whether one state is reachable from another via the existence of an action trajectory . It may be helpful to review the reachable set definitions from Section 14.2.1.