Optimal Model Approximation of Discrete-Time T-S Fuzzy Systems: Hankel Norm Approach

This paper is concerned with the Hankel norm model approximation for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delay. For a given stable T-S fuzzy system, our attention is focused on the construction of a reduced-order model which not only approximates the original system well with a Hankel norm performance but also is translated into a lower-dimensional system. By employing the modified delay partitioning method, a delay-dependent sufficient condition is developed for the asymptotic stability with a Hankel norm error performance for the error system. Then, the Hankel norm approximation problem is solved by employing the convex linearization approach, which cast the reduced-order model construction into a convex optimization problem subject to linear matrix inequality constraints. Finally, a numerical example is provided to show the effectiveness of the proposed methods.