Partial state bounding with a pre‐specified time of non‐linear discrete systems with time‐varying delays

In this study, the authors address a new problem of finding, with a pre‐specified time, bounds of partial states of non‐linear discrete systems with a time‐varying delay. A novel computational method for deriving the smallest bounds is presented. The method is based on a new comparison principle, a new algorithm for finding the infimum of a fractal function, and linear programming. The effectiveness of our obtained results is illustrated through a numerical example.