Robust detectability from the measurements plus state feedback stabilization imply semiglobal stabilization from the measurements

We study the problem of stabilizing with large regions of attraction a general class of nonlinear system consisting of a linear nominal system plus uncertainties. A similar result was given by the same author in previous works; in this paper we prove that what was referred in these works to as "nonlinear coupling condition" can be reformulated in the control design as a "nonlinear rescaling" of the Lyapunov functions of the closed-loop system plus the requirement for a suitably faster convergence of the state estimation error. We obtain a paradigm very similar to the linear case, for which if a couple of Hamilton-Jacobi inequalities (state feedback and observer design) are satisfied then a measurement feedback stabilizing controller can be readily found. Our result is particularly useful for those systems which are not uniformly completely observable (UCO) due to uncertainty or disturbances. Examples are given for showing improvements over the existing literature