Observer Design for Takagi-Sugeno Fuzzy Systems Using Poly-Quadratic Lyapunov Function Based On Lipschitz Approach

In this work, a contribution to reduce the conservatism of the observers for Takagi-Sugeno fuzzy systems with unmeasurable premise variables (UPV) based on the Lipschitz assumption compared to previous work is proposed. In order to achieve this goal, the poly-quadratic Lyapunov function (PQLF) along with a good employment of the completion of squares property are used. The proposed method helps in reducing the conservatism that arises when the Lipschitz constant exceeds an admissible value and when the quadratic approach becomes infeasible. The stability conditions are presented as Linear Matrix Inequalities (LMIs), ensuring the asymptotic convergence of the state estimation error. A numerical illustration is provided to demonstrate the feasibility of the proposed work.