On Robust Feedback for Systems with
Multidimensional Control

V.I. Korobov and T.V. Revina

Department of Applied Mathematics, School of Mathematics and Computer Science, V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv 61022, Ukraine
E-mail: vkorobov@univer.kharkov.ua t.revina@karazin.ua

Received June 1, 2016, revised October 11, 2016

Abstract

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.