This article deals with the stability analysis of Lure type systems through aperiodic sampled‐data control laws, where the nonlinearity is assumed to be both sector and slope restricted. The proposed method is based on the use of a new class of looped‐functionals, which depends on the nonlinearity and its slope, and on a generalized Lure type function, that is quadratic on both the states and the nonlinearity and has a Lure‐Postnikov integral term. On this basis, conditions in the form of linear matrix inequalities to certify global or regional asymptotic stability of the closed‐loop system are obtained. These conditions are then used in optimization problems for computing the maximum intersampling interval or the maximum sector bounds for which the stability of the sampled‐data closed‐loop system is guaranteed. Numerical examples to illustrate the results are provided.