State and disturbance observer-based controller synthesis for polynomial system

This paper proposes a new method for designing an observer-based controller for the polynomial system with the existence of the disturbances. A new form of the observer is proposed to estimate both unavailable state variables and disturbances simultaneously. In addition, in previous studies, the disturbances must be bounded, its derivation is equal to zero, or assume to be generated by an exogenous system. However, in this paper, the arbitrary disturbances are considered and they do not need to satisfy any constraint. Based on the information of unknown states and disturbances from observer, a controller is synthesized to eliminate the effects of disturbances and stabilize this system. On the basis of SOS technique and Lyapunov theory, the conditions for observer-based controller design are derived. Finally, an illustrative example is presented to prove the effectiveness of the proposed method.