Time-varying feedback for the global stabilization of nonlinear systems with measurement disturbances

We consider the problem of globally asymptotically stabilizing a nonlinear system and furthermore rendering it input-to-state stable (ISS) with respect to additive measurement disturbances. As time-invariant feedback cannot achieve such stability in general (even when such feedback suffices in the absence of measurement disturbances), we explore the possibility of using time-varying feedback to solve the problem. Rather than attack the problem directly, we will examine simpler stabilization problems which have been shown to be closely related to the problem of interest. First, we construct a a periodic time-varying feedback law for a general class of scalar nonlinear systems which provides the desired ISS property and depends only on the magnitude of the measurement. We then present some related results for a class of higher-dimensional nonlinear systems.