Controlled invariant subspace

A subspace V is called controlled invariant if for any x₀ of V and an input u, $x_{u}(t,x_{0})$ is in V, for all nonnegative t.

Properties

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