Design of an Observer-Based Controller for T-S Fuzzy Time-Delay Systems under Imperfect Premise Matching

In this paper, the stabilization problem of an observer-based T-S fuzzy time-delay system under imperfect premise matching is studied, in which the T-S fuzzy observer model with time-delay and the fuzzy controller do not share the same membership functions. The objective is to design a state observer and un-matching fuzzy controller such that the closed-loop system with time-delay is asymptotically stable. A sufficient condition for the stabilization via observer-based state feedback under imperfect premise matching is presented, and an observer-based state feedback controller under imperfect premise is also constructed. The proposed control scheme is well capable of enhancing the design flexibility, because the membership functions of the observer-based controller can be arbitrarily selected. A few numerical examples are given to illustrate the effectiveness and advantages of our design method.