We extend the separation results of a previous work of ours (1999) to a case where a globally bounded state feedback controller renders a certain compact set positively invariant and asymptotically attractive. The extension covers a wide range of control tasks that arise in adaptive control, servomechanisms, and practical stabilization. It is shown that by implementing the control law using a high-gain observer, we can recover the performance of the state feedback controller.
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Atassi et al. (2001) studied this question.
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