// Workers AI · dad joke modeWhat did hyperstability say to instability? You're unstable, I'm hyper.

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 $k_{1}\geq 0,k_{2}\geq 0$ such that any state trajectory of the system satisfies the inequality:

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

See also

• Stability theory
• BIBO stability