An LMI-based global non-quadratic observer design via Takagi-Sugeno models and Levant's robust differentiators

Abstract

An innovative solution for global non-quadratic observer design of nonlinear systems is presented in this report. Via an exact convex representation of the model in the Takagi-Sugeno form, an observer which employs the nonlinearities of the system as well as a discontinuous function of their time derivatives, is proposed. It is shown that such a structure, when combined with a non-quadratic Lyapunov function, enhances former results by reaching global conditions up to the modeling region, while being able to deal with the time derivatives of the nonlinearities in the Lyapunov function. The required derivatives are obtained in finite-time from an s-th order Levant's robust differentiator, which better fits with the discontinuous nature of the observer. Design conditions are expressed as linear matrix inequalities. Examples are provided that show the advantages as well as the limitations of the novel approach.