$H_\infty $ Observer Design for Continuous-Time Takagi–Sugeno Fuzzy Model With Unknown Premise Variables via Nonquadratic Lyapunov Function

This paper deals with the problem of observer design for continuous-time Takagi-Sugeno fuzzy models with unmeasurable premise variables. First, in order to improve the existing results of observer design, a new method is proposed to bound the time derivatives of the membership function. Then, by applying the nonquadratic Lyapunov function and the matrix decoupling technique, the controller gains and observer gains are designed to guarantee that the error system is asymptotically stale. Furthermore, better H∞ performance can be obtained by solving an optimization problem. All of the results are presented as linear matrices inequalities and three examples are provided to demonstrate the merits of the proposed approach.