Low gain and low-and-high gain feedback: A review and some recent results

Abstract

Low gain feedback refers to a family of stabilizing state feedback gains that are parameterized in a scalar and go to zero as the scalar decreases to zero. Low gain feedback was initially proposed to achieve semi-global stabilization of linear systems subject to input saturation. It was then combined with high gain feedback in different ways for solving various control problems. The resulting feedback laws are referred to as low-and-high gain feedback. Since the introduction of low gain feedback in the context of semi-global stabilization of linear systems subject to input saturation, there has been effort to develop alternative methods for low gain design, to characterize key features of low gain feedback, and to explore new applications of the low gain and low-and-high gain feedback. This talk reviews the developments in low gain and low-and-high gain feedback designs. Most of the results mentioned in the talk have appeared in the literature. A few recent results are still under review for publication.