Observer design for Takagi–Sugeno systems with unmeasurable premise variables using a non-quadratic Lyapunov function

Abstract

This work presents a contribution to reduce the conservatism in nonlinear observer for TakagiSugeno fuzzy systems with unmeasurable premise variables based on the mean value theorem. The conservatism was reduced through the use of non-quadratic Lyapunov function (NQLF) rather than the quadratic form used in previous works. The stability conditions are given in the form of Bilinear Matrix Inequalities (BMI) whereby an effective solution to solve this type of problem is presented using linear solvers which are characterized by their computational efficiency. To show the improvement of the proposed work over the existing approach and to demonstrate its effectiveness in solving the Bilinear Matrix Inequalities, the feasibility area is illustrated by a numerical example, and a real-time implementation of the observer is applied to the induction motor (IM) where a big number of inequalities is present.