A class of discrete-time non-linear positive time-delay switched systems with sector-type non-linearities is studied. Sufficient conditions for the existence of common and switched diagonal Lyapunov-Krasovskii (L-K) functionals for this system class are derived; these are expressed as feasibility conditions for systems of linear algebraic inequalities. Corresponding spectral conditions for the existence of common L-K functionals are also described. Furthermore, it is shown that the proposed approaches can be applied to discrete-time models of digital filters and neural networks. Finally, a numerical example is given to illustrate the effectiveness of theoretical results.