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+<br>In this article, being totally different from standard time-discretization (merely called discretization) formulas, explicit linear left-and-proper [5 Step Formula](http://aqp.kr/m/bbs/board.php?bo_table=free&wr_id=51690)-step (ELLR5S) formulas with sixth-order precision are proposed. The general sixth-order ELLR5S method with 4 variable parameters is developed first, and  [5 Step Formula Review](http://skupra-nat.uamt.feec.vutbr.cz:30000/eldonhilson308/7118832/-/issues/7) constraints of these four parameters are displayed to ensure the zero stability, consistence, and convergence of the components. Then, by choosing specific parameter values inside constraints, eight particular sixth-order ELLR5S formulas are developed. The overall sixth-order ELLR5S components is additional utilized to generate discrete zeroing neural community (DZNN) models for  [5 Step Formula](http://git.bkdo.net/brianmccollom/95575-step-formula/-/issues/1) solving time-varying linear and nonlinear systems. For comparison, three conventional discretization formulas are additionally utilized. Theoretical analyses are introduced to indicate the performance of ELLR5S formulation and DZNN models. Moreover, considerable experiments, together with three practical purposes, that's, angle-of-arrival (AoA) localization and two redundant manipulators (PUMA560 manipulator and Kinova manipulator) management, are conducted. The synthesized results substantiate the efficacy and superiority of sixth-order ELLR5S formulation as properly as the corresponding DZNN fashions.<br>
+
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