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 note, 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 Riccati-like inequalities (state feedback and observer design) are satisfied then a measurement feedback stabilizing controller can be readily found. Examples are given for showing improvements over the existing literature