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.[1]

Definition:[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} {\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} {\displaystyle \|x(t)\|<k_{1}\|x(0)\|+k_{2},\,\forall t\geq 0}

References

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

See also