In this note, we extend the separation results of a previous work to a case
where a globally bounded state feedback controller renders a certain compa
ct set positively invariant and asymptotically attractive. The extension co
vers a wide range of control tasks that arise in adaptive control, servomec
hanisms, and practical stabilization. It is shown that by implementing the
control law using a high-gain observer, we can recover the performance of t
he state feedback controller.