Hyperstability
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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.cite-ref-anderson-1-0[1]
Definition:cite-ref-zinober-2-0[2] A system is hyperstable if there are two constants k 1 ≥ ≥ 0 , k 2 ≥ ≥ 0 {\displaystyle 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 , ∀ ∀ t ≥ ≥ 0 {\displaystyle \|x(t)\|<k_{1}\|x(0)\|+k_{2},\,\forall t\geq 0}
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References
cite-note-anderson-11. ↑ Brian D. O Anderson, "A Simplified Viewpoint of Hyperstability", IEEE Transactions on Automatic Control, June 1968
cite-note-zinober-22. ↑ Zinober, Deterministic control of uncertain systems, 1990
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