In this paper we consider the problem of evaluating the performance of state feedback H∞ controllers for a class of nonlinear systems with respect to the domain of validity. The class under study is a generalization of the well-known Lur'e systems. The set of controllers is derived from a class of storage functions of the Lur'e-Postnikov type whose integral term is parameterized by a nonlinear scalar function. A geometrical interpretation of the validity domain of such controllers is proposed, along with easy-to-check conditions for global stabilization and L2 performance requirement satisfaction. A simple test for global validity of linear controllers is also given.