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Abstract: This paper investigates stabilization of single-input nonlinear systems by switching between two separate nonlinear feedback controllers. The first, a pseudolinear controller, provides a region of attraction $R0$ around the equilibrium manifold. The second controller is high-gain, and is designed to drive the state originating in a (larger) set of initial conditions $R1$ into $R0$. When the state enters $R0$, the control is switched from the high-gain control to the pseudolinear control. Simple analytic estimates of both $R0$ and $R1$ are given. The method is applied in simulation to an acrobot, and in simulation and experiment to a rotating inverted pendulum.