Robust feedback synthesis for the canonical system

Abstract

The paper deals with the problems of global and local robust feedback synthesis of bounded control for a system with unknown bounded perturbation. Our approach is based on the method of controllability function proposed by V. I. Korobov. The ranges of perturbations are found from the condition that the total derivative of the controllability function caused by the perturbed system must be negative. We determine the largest segment of variation of the perturbation and construct a positional control that steers an arbitrary initial point to the origin within a finite period of time. The length of this period is estimated both from below and from above. A two-dimensional system is considered as an example.