Solution of the H-infinity steady-state Riccati equation for non exponentially stabilizable systems

In the H-infinity, framework, the solution of the steady-state Riccati equation (SSRE) is a necessary and sufficient condition for the existence of a bounded state feedback control ensuring internal stability and disturbance attenuation in the closed-loop system. The existence of such a solution is usually investigated under the assumption of the system's exponential stabilizability. This property is not met for a class of models arising in a large set of applications such as the control of mechanical structures with distributed flexibility. In this paper is shown that the solution of the H-infinity SSRE admits the sought solution for the class of non exponentially stabilizable systems modeling flexible structures with damping.