Model approximation for discrete-time state-delay systems in the TS fuzzy framework

This paper is concerned with the problem of ℋ_∞ model approximation for discrete-time TakagiSugeno (T-S) fuzzy time-delay systems. 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 in an ℋ_∞ performance but is also translated into a linear lower dimensional system. By applying the delay partitioning approach, a delay-dependent sufficient condition is proposed for the asymptotic stability with an ℋ_∞ error performance for the error system. Then, the ℋ_∞ model approximation problem is solved by using the projection approach, which casts the model approximation into a sequential minimization problem subject to linear matrix inequality (LMI) constraints by employing the cone complementary linearization algorithm. Moreover, by further extending the results, ℋ_∞ model approximation with special structures is obtained, i.e., delay-free model and zero-order model. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.