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 $k_1\ge 0,k_2\ge 0$ such that any state trajectory of the system satisfies the inequality:

$\Vert x(t)\Vert <k_1\Vert x(0)\Vert +k_2,\mathrm{\forall }t\ge 0$

See also

• Stability theory
• BIBO stability

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