Using the decomposition principle to stabilize the nominal motion of a mechanical system with given accuracy

The Pyatnitskii decomposition principle is used to stabilize the nominal motion of a controllable scleronomic holonomic mechanical system under the influence of a bounded perturbing force. We find conditions on the controlling force and the set of initial states that guarantee that the motion of this mechanical system occurs close to the nominal motion in such a way that deviations from nominal values lie inside given boundaries. The decomposition principle serves here as an instrument to ensure practical stability in the sense of La Salle and Lefshetz.