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

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

Hyperstability

See also