Hyperstability Explained

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

See also

• Stability theory
• BIBO stability

Notes and 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