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

Abstract

AbstractIn 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, , 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.