Robust observer design for uncertain polynomial systems

Abstract

This research proposes a new method to synthesize a robust observer for the polynomial systems in the presence of the uncertainties. Here, a special mathematical transformation is carried out to convert the uncertain polynomial systems into the unknown input polynomial systems and then the robust observer is designed for estimating the state variables of these systems. Moreover, unlike the existing papers where the bounded conditions of the uncertainties must be given, in this paper, the bounded constraints of the uncertainties are not known in advance and the influences of uncertainties are completely eliminated without using a controller or other techniques. Additionally, a new form of an observer is presented to reduce the complexity of derivation and make the observer synthesis procedure be more relaxed. On the basis of Lyapunov theory and Sum of Square (SOS) technique, the conditions for observer synthesis are derived. Finally, a numerical example is shown to prove the effectiveness of the proposed method.