The subject of stability addresses properties of a vector field with respect to a given point. Let denote a smooth manifold on which the vector field is defined; may be a C-space or a phase space. The given point is denoted as and can be interpreted in motion planning applications as the goal state. Stability characterizes how is approached from other states in by integrating the vector field.
The given vector field is considered as a velocity field, which is represented as
(15.1) |