The discrete-time uncertain nonlinear models are considered in a Takagi-Sugeno form and their stabilization is studied through a nonquadratic Lyapunov function. The classical conditions consider a one-sample variation, here, the main results are obtained considering k samples variation, i.e., Delta V-k(x(t)) = V(x(t + k)) - V(x(t)). The results are shown to always include the classical cases, and several examples illustrate the effectiveness of the approach.