# On the Steady State Motions Control Problem for Mechanical Systems with Relay Controllers

## DOI:

https://doi.org/10.52846/stccj.2021.1.1.10## Keywords:

differential equation with discontinuous right-hand side, stability, mechanical system, steady state motion stabilization## Abstract

The paper presents the solution to the stabilization problem of steady state motions for a holonomic mechanical system by using relay controllers. This solution is achieved by proving new theorems on the asymptotic stability of the solution to a differential equation with a discontinuous right-hand side. The novelty of the theorems is based on the limiting inclusions construction and the use of semidefinite Lyapunov functions. As an example, the stabilization problem of steady-state motion for a five-link robot manipulator is solved by using relay controller.

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*Syst. Theor. Control Comput. J.*, vol. 1, no. 1, pp. 48–55, Jun. 2021, doi: 10.52846/stccj.2021.1.1.10.