$H\infty$ LMI-Based Observer Design for Nonlinear Systems via Takagi–Sugeno Models With Unmeasured Premise Variables

This paper is concerned with state estimation for continuous-time nonlinear systems. By means of a polytopic exact representation of the system using interpolation functions whose premise variables can be unmeasured, the differential mean value theorem and a quadratic Lyapunov function are used to provide conditions in the form of linear matrix inequalities, guaranteeing the state estimation error to be asymptotically driven to zero. A robust extension of the proposed observer design performing $H\infty$ disturbance rejection is also presented. Examples illustrating the effectiveness of the developed novelties against former results are included.