Wikipedia
Hyperstability
In stability theory, hyperstability is a property of a system that requires the state vector to remain bounded if the inputs are restricted to belonging to a subset of the set of all possible inputs.
Definition: A system is hyperstable if there are two constants k ≥ 0, k ≥ 0 such that any state trajectory of the system satisfies the inequality:
∥x(t)∥ < k∥x(0)∥ + k, ∀t ≥ 0