The state estimation of linear systems has well-established approaches in the literature, whereas, for nonlinear systems, several methodologies have been proposed to overcome the various difficulties encountered in obtaining a sub-optimal solution, according to some criterion. This work presents a nonlinear filter approach that guarantees robustness to unknown exogenous signals. The methodology consists of treating the incompatibility of unmeasurable nonlinearities, present in the model, in a convex way. With this representation, it is possible to derive conditions based on convex optimization, by means of Linear Matrix Inequalities (LMIs), to achieve the design objectives. The example illustrates the preliminary results of the proposed methodology.