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.[1]

Definition:[2] 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

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


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