H-infmity disturbance rejection for nonlinear systems is considered in this paper. Based on an exact representation of the system in the form of a Takagi-Sugeno model as well as on the key matrix properties of Finsler's Lemma and Peaucelle transformation, two alternative control laws are proposed. These control laws extend and generalize the well-known parallel distributed compensation by using nested convex sums in two progressively more general structures. It is proved the proposed schemes allow combining the simplicity of the quadratic Lyapunov function with arbitrarily complex control laws, thus achieving significant improvements over existing approaches while avoiding the common problem of handling the time derivatives of the membership functions. The results thus obtained are expressed as linear matrix inequalities up to a logarithmically searchable parameter. Several examples show the advantages of the contributions.