This paper deals with the problem of robust stabilization of an uncertain nonlinear system with output measurements using the invariant ellipsoid method. The non-linear system is uncertain but bounded according to a dasiaquasi-lipschitzpsila condition and the output measurements are subjected to perturbations bounded by ellipsoids.The invariant ellipsoid method allows to obtain the robust linear feedback as a solution of the special linear optimization problem with bilinear constraints. The methods for solving this optimization problem involves the LMI technique. The stabilization of the double mass-spring system is considered as an illustrative example.