An Efficient Lyapunov Function for Discrete T–S Models: Observer Design

This paper deals with the design of a new observer synthesis for discrete Takagi-Sugeno (T-S) fuzzy models. It is well established that quadratic synthesis for discrete T-S models and/or linear parameter-varying systems can be outperformed easily via nonquadratic syntheses. Several Lyapunov functions can be used. Nevertheless, this paper shows that with a “small” change in the initial Lyapunov function, a “better” (in the sense of solutions to the linear matrix inequality constraints problem) Lyapunov function can be reached. This one can introduce very important improvements.