Global internal stabilizability does not imply global external stabilizability for small sensor disturbances

It was shown by Sontag (ibid., vol.34, no.4, p.435-43 (1989)) that for control-affine nonlinear systems, global asymptotic stabilizability via continuous state feedback implies global input-to-state stabilizability with respect to actuator disturbances. We show that the analogous result for sensor disturbances does not hold: we construct a second-order system which admits a continuous memoryless globally asymptotically stabilizing state feedback controller but for which no such controller can prevent finite escape times from every initial condition in the presence of small sensor disturbances.