Distance to the Viable Set (or Viability Distance)

Definition:

This is the distance between a given state xxx and the set of viable states V.

Formula:

$$
d(x, \mathcal{V}) = \inf_{y \in \mathcal{V}} \| x - y \|
$$
 

Usefulness:

The greater this distance, the further the state is from the viability conditions; it therefore measures how much a system is "at risk" of exceeding the viable constraints.