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.^[1]

Definition:^[2] A system is hyperstable if there are two constants ${\displaystyle k_{1}\geq 0,k_{2}\geq 0}$ such that any state trajectory of the system satisfies the inequality:

${\displaystyle \|x(t)\|<k_{1}\|x(0)\|+k_{2},\,\forall t\geq 0}$