Riccati equations for strongly stabilizable bounded linear systems

We obtain necessary and sufficient conditions for the existence of strongly stabilizing solutions to Riccati equations for infinite-dimensional systems that are strongly, but not exponentially stabilizable. We apply the theory to derive a Riccati criterion for the existence of J-spectral factorizations and illustrate it by proving the strict positive real and bounded real lemmas for a class of strongly stable systems with collocated actuators and sensors. (C) 1998 Elsevier Science Ltd. All rights reserved.