On robust feedback for systems with multidimensional control

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