Implicit-Euler based digital implementation for constrained stabilization of second-order systems

Abstract

In this article, an implicit Euler algorithm for digital implementation of constrained stabilization is studied for the second-order systems. For that, a switching controller is designed in a discrete-time framework such that the system's position output converges to some predefined range, that is, ϱ ∈ (−ε, ε) in finite-time while the velocity output converges to the origin, that is, (Formula presented.), in finite-time. The switching controller is switched to the implicit Euler implementation of twisting algorithm when ϱ ∉ (−ε, ε) and to an implicit Euler implementation of first-order sliding mode control when ϱ ∈ (−ε, ε). The combination of the two implicit Euler implementations achieves discrete-time constrained stabilization of second-order systems, avoiding the chattering caused by conventional explicit integration schemes. The usefulness of the proposed algorithm for constrained stabilization is illustrated by considering the container-slosh coupled dynamical system. © 2021 John Wiley & Sons Ltd.