Fuzzy observer and fuzzy controller design for a class of uncertain non‐linear systems

In this study, a fuzzy state observer and a fuzzy controller are developed for a class of uncertain non‐linear systems, which are represented through a set assumptions of matrix inequalities. Many original investigations and results are obtained. First, by constructing a class of Lyapunov functions and the introduced matrix inequalities tools, the adaptive observer laws including new Ricatti equations, two differentiators and many solvability conditions about the obtained Ricatti equations are presented. Second, based on another class of Lyapunov functions and the same matrix inequalities tools, the proposed controllers are designed to guarantee the stability of the overall closed‐loop systems, and many solvability conditions on the proposed controllers are analysed too. Finally, numerical simulations on the single‐input single‐output magnetic levitation systems show the effectiveness of these approaches. The above work allows to provide further applications on the proposed observer and controller designs without resorting to universal fuzzy approximation.