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A theorem on global stabilization of nonlinear systems by linear feedback. (English) Zbl 0749.93071

Summary: We investigate the global stabilizability problem for a wide class of single-input nonlinear systems whose the linearization at the equilibrium is controllable. We show that under general assumptions there exists a linear feedback law which globally exponentially stabilizes the system at its equilibrium. The proof of our main theorem is based on some ideas from a previous paper. We use the theorem to recover a recent result of Gauthier et al. concerning the observer design problem.

MSC:

93D15 Stabilization of systems by feedback
93C10 Nonlinear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
93B07 Observability
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