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Positively invariant set

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In mathematical analysis, a positively (or positive) invariant set is a set with the following properties:

Suppose is a dynamical system, is a trajectory, and is the initial point. Let where is a real-valued function. The set is said to be positively invariant if implies that

In other words, once a trajectory of the system enters , it will never leave it again.

References

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  • Dr. Francesco Borrelli [1]
  • A. Benzaouia. book of "Saturated Switching Systems". chapter I, Definition I, Springer 2012. ISBN 978-1-4471-2900-4 [2].