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Controlled invariant subspace

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Controlled Invariant Subspace A subspace V is called controlled invariant , if for any x0 of V and such an input u, xu(t,x0) is in V , for all t nonnegative.

Theorem: Let V be a subspace of X.Then the following are equivalent
i)V is controlled invariant
ii)AV is in V + Im B
iii)There exist a feedback F such that (A+BF)V is in V

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