In this article, being completely different from conventional time-discretization (simply referred to as discretization) formulas, specific linear left-and-proper 5 Step Formula-step (ELLR5S) formulas with sixth-order precision are proposed. The final sixth-order ELLR5S formula with four variable parameters is developed first, and 5 Step Formula constraints of those 4 parameters are displayed to ensure the zero stability, consistence, and convergence of the system. Then, by choosing specific parameter values within constraints, eight particular sixth-order ELLR5S formulation are developed. The overall sixth-order ELLR5S simple income method is further utilized to generate discrete zeroing neural network (DZNN) models for fixing time-varying linear and nonlinear systems. For comparison, three standard discretization formulas are also utilized. Theoretical analyses are offered to indicate the performance of ELLR5S formulation and DZNN models. Furthermore, plentiful experiments, together with three practical applications, 5 Step Formula that's, angle-of-arrival (AoA) localization and two redundant manipulators (PUMA560 manipulator and Kinova manipulator) control, are carried out. The synthesized outcomes substantiate the efficacy and superiority of sixth-order ELLR5S formulas as properly because the corresponding DZNN fashions.

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