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.
Mathematics Subject Classification 2000: 93B50, 93D09, 93C73, 70Q05. Key words: controllability function method, systems with multidimensional control, robust feedback synthesis, finite-time stabilization, unknown bounded perturbations, uncertain systems.
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