State Observer Design for a Class of Rational Nonlinear Systems

This paper presents a novel methodology for the synthesis of state observers for a class of systems subject to rational nonlinearities. The key idea is to represent both the system and the observer in the so-called differential-algebraic representation in order to obtain the error dynamics. Once achieved, design conditions can be formulated through optimization problems subject to constraints in the form of linear matrix inequalities. This approach enables the development of a systematic observer design framework with formal theoretical guarantees, including the asymptotic stabilization of the error within a specified exponential decay rate along with constraints on the observer gains. A post-synthesis analysis is presented to ensure the stability of the plant considering the feedback of the estimated states. An illustrative example is provided to showcase the proposed method.