Summary: 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, \(\varrho\in(-\varepsilon,\varepsilon)\) in finite-time while the velocity output converges to the origin, that is, \(\dot{\varrho}=0\), in finite-time. The switching controller is switched to the implicit Euler implementation of twisting algorithm when \(\varrho\not\in(-\varepsilon,\varepsilon)\) and to an implicit Euler implementation of first-order sliding mode control when \(\varrho\in(-\varepsilon,\varepsilon)\). 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.
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