On robust feedback for systems with multidimensional control

The paper deals with local robust feedback synthesis for systems with multidimensional control and unknown bounded perturbations. Using V.~I.~Korobov's controllability function method, we construct a bounded control which steers an arbitrary initial point to the origin in some finite time; an estimate from above for the time of motion is given. We have found the range of a segment where the perturbations can vary. As an example we consider the problem of stopping the oscillations of the system of two coupled pendulums.