A separation principle for the control of a class of nonlinear systems

We give a general formulation of a number of control problems. This formulation considers a wide class of systems and any globally bounded state feedback controller that renders a certain compact set positively invariant and asymptotically attractive. We develop a converse Lyapunov theorem, and we prove that, by implementing the control law using a high-gain observer, we can recover asymptotic stability of the attractive set, its region of attraction, and trajectories