Abstract
The set of negative-semidefinite solutions of the algebraic Riccati equation A∗X + XA + XBB∗X − C∗C = 0 is studied under the most general hypothesis, namely that (A, B) is stabilizable modulo the undetectable subspace of (A, C). If is a lattice, then is isomorphic to 0 ⊕ S where T0 is the direct sum of copies of the set of nonnegative real numbers and is a closure of which is order isomorphic to a system of well-defined A-invariant subspaces. Necessary and sufficient conditions are given such that (or) is a lattice.
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