Isolated nonnegative solutions of infinite-dimensional algebraic Riccati equations

For an infinite-dimensional continuous (or discrete)-time linear system, ba sed on the study of the representation of nonnegative solutions of the alge braic Riccati equation (ARE), we get some sufficient and necessary conditio ns for a nonnegative solution of(ARE) to be isolated in the set of all nonn egative solution of (ARE) with respect to the norm topology, the strong ope rator topology and weak operator topology, respectively. (C) 1999 Elsevier Science B.V. All rights reserved.