Relaxed Conditions of Observer Design of Discrete-Time Takagi–Sugeno Fuzzy Systems via a New Multi-Instant Gain-Scheduling Scheme

A novel multi-instant gain-scheduling scheme is proposed in order to further improve the state estimation performance of discrete-time Takagi–Sugeno fuzzy systems in this article. Different from those existing methods, the enabled working pattern at each sampling instant can be determined in cycle according to utilization of the updated information of adjacent normalized fuzzy weighting functions in depth, and then the featured time-varying free matrices are introduced for each working pattern, which can remove those existing constraints on traditional free matrices. Consequently, the conservatism can be reduced significantly and it does broaden the range of application for observer-based fuzzy state estimation. Despite the fact that the quantity of the free matrices becomes much bigger than before, it needs to be pointed out that the actual computational complexity only increases by a small amount through depressing the number of cycles. Given that the developed designing process belongs to an offline computation, it is an acceptable tradeoff between the increasement of computational burdens and the reduction of conservatism. In the end, the effectiveness of the developed method is illustrated through the detailed analysis of numerical simulations.