Hankel norm model approximation of Takagi–Sugeno fuzzy time-delay systems

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 is also 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 casts 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.