About step-length of ZeaD (Zhang et al Discretization) formula 4IgS_Y for future minimization via fan equations

Abstract

Future minimization, i.e., discrete time-varying minimization, is a difficult and meaningful problem. It has been successfully solved by Zhang et al using zeroing dynamics (ZD) and discretization formulas. In this paper, a type of discrete-time ZD (DT-ZD) model, which is obtained via utilizing ZeaD (Zhang et al Discretization) formula 4IgS_Y, is analyzed and investigated to ensure its stability. Specifically, via theoretical guarantees, we propose the step-length domain, or say, the effective domain of the step-length, which makes the discrete-time model stable. Additionally, we make further efforts to obtain the step-length optimum which provides the optimal stability of the DT-ZD model. Eventually, numerical experiments are performed to validate the step-length domain and the step-length optimum of the DT-ZD model for future minimization.