Definition:
This is the set of initial states from which there exists at least one feasible trajectory satisfying the constraints for all future times.
Formally:
$$
\text{Viab}_F(K) = \left\{ x_0 \in K \,\middle|\, \exists \ x(t), \ \dot{x}(t) \in F(x(t)), \ x(t) \in K, \ \forall t \geq 0 \right\}
$$
Usefulness:
This indicator is crucial: it allows us to identify the "safe zone" of the system in the long term.