An optimal feedback approach for the stabilization of linear systems subject to input saturation and magnitude-bounded disturbances

Abstract

Disturbance may severely degrade the control accuracy of an input-saturated system and even induce instability. This paper intends to present an approach to realize optimal disturbance attenuation for an input-saturated system subject to magnitude-bounded disturbance. Based on circle criterion and the techniques of linear matrix inequalities and convex optimization, stability properties of a system under a known feedback controller are analyzed and an linear approach of synthesizing optimal feedback controller is proposed. Illustrative examples are given and state trajectories of the system before and after stabilization are compared to examine the effectiveness of the proposed approach. The simulation results show that the synthesized controller is effective in stabilizing the system and realizing optimal disturbance attenuation. © 2013 Springer-Verlag Berlin Heidelberg.