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A separation principle for the control of a class of nonlinear systems. (English) Zbl 1055.93064
The note extends separation results [A. N. Atassi and H. K. Khalil, IEEE Trans. Autom. Control 44, 1672–1687 (1999; Zbl 0958.93079)] for the stabilization of a class of nonlinear systems having a chain or more of integrators and where feedback controllers make the origin of the closed-loop system an asymptotically stable equilibrium to the case where a globally bounded state feedback controller renders a certain compact set that is positively invariant and asymptotically attractive. This extension covers a wide range of control problems that arise in adaptive control, servomechanisms, and practical stabilization. It is shown that by implementing the control law using a high-gain observer, one can recover the performance of the state feedback controller. As an illustration, the separation theory developed in the paper is applied to a certain regulation problem.

MSC:
93D15 Stabilization of systems by feedback
93C10 Nonlinear systems in control theory
93C70 Time-scale analysis and singular perturbations in control/observation systems
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