Strong stabilizability and the steady state Riccati equation

We explore strong stabilizability (as opposed to exponential stabilizability) with the aid of the steady state Riccati equation. We show that the latter can have at most one strongly stable solution and obtain some sufficient conditions for existence. We also indicate an application to steady state Kalman filtering where the observation operator is compact so that we may not have exponential stability.Research supported in part under Grant No. 78-3550, AFOSR, USAF, Applied Math Division.