stability theory In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial diffe ...

, 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.Brian D. O Anderson, "A Simplified Viewpoint of Hyperstability", ''IEEE Transactions on Automatic Control, June 1968'' Definition:Zinober, Deterministic control of uncertain systems, 1990 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: :

\,  x(t) \,  < k_1 \, x(0)\,  + k_2, \, \forall t \ge 0

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