Local Stability Analysis and Estimation of Domains of Attraction for Discrete-Time Takagi-Sugeno Fuzzy Systems via Fuzzy-Modeled Membership Functions

This paper addresses the problem of local stability analysis and estimation of the region of attraction for discrete-time Takagi-Sugeno fuzzy systems. A fuzzy-modeling approach is used to obtain a polytopic representation of the membership functions in terms of the premise variables. Unlike other methods available in the literature, this representation eliminates the need for information - in general given in terms of bounds - about the variation of the membership functions. Consequently, the estimation of the domain of attraction becomes a single-parameter minimization problem subject to linear matrix inequality constraints. To demonstrate the effectiveness of the approach, the paper provides numerical examples including a comparison with another method from the literature.