Quasihomogeneous Stabilization of Fully Actuated Systems with Dry Friction

Abstract

Quasihomogeneity-based synthesis appears to be extremely suited for fully actuated systems with dry friction. This claim is supported by several arguments. Firstly, mechanical systems with relatively strong Coulomb friction require discontinuous controllers for adequate regulation. Secondly, external disturbances, affecting these systems, meet the matching condition so that their influence on the underlying system is not simply attenuated as it would be the case under ℋ_∞-synthesis, but it is also rejected under the quasihomogeneous synthesis. Thirdly, the global position regulation becomes possible provided that an upper bound on the magnitude of the external disturbances is known a priori. These features are subsequently illustrated by means of the orbitally stabilizing synthesis of a simple inverted pendulum and by means of the global position regulation of a multi-link robot manipulator.