Pre-specified performance based model reduction for time-varying delay systems in fuzzy framework

This paper attempts to provide a new solution to the model approximation problem for dynamic systems with time-varying delays under the fuzzy framework. For a given high-order system, our focus is on the construction of a reduced-order model, which approximates the original one in a prescribed error performance level and guarantees the asymptotic stability of the corresponding error system. Based on the reciprocally convex technique, a less conservative stability condition is established for the dynamic error system with a given error performance index. Furthermore, the reduced-order model is eventually obtained by applying the projection approach, which converts the model approximation into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.