Positive invariant set

Positive invariant set

A positive invariant set is a set with the following properties:

Given a system dot{x}=f(x) and trajectory x(t,x_0) , where x_0 , is the initial point. Let mathcal{O} riangleq left lbrace x in mathbb{R}^n| phi (x) = 0 ight brace where phi is a real valued function that characterizes mathcal{O}. The set mathcal{O} is said to be positively invariant if x_0 in mathcal{O} implies that x(t,x_0) in mathcal{O} forall t ge 0

References

*Dr. Arun D. Mahindrakar [http://www.ee.iitm.ac.in/~arun_dm/reports/positive_invariant.pdf]


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