A peak-to-peak filtering for continuous Takagi-Sugeno fuzzy systems by a local method

We investigate the peak-to-peak filtering problem for continuous Takagi-Sugeno fuzzy systems. First, a novel filter, where the premise variables depend partly on the output of the filter, is constructed and the corresponding filtering error system is obtained. Then, a new approach, which is called the local approach, is developed for the filtering error system. Here, the local approach means that the state trajectories of the filtering error system are restricted to a compact set such that the deviations between the normalized membership functions of the system and those of the filter have prescribed upper bounds. Then, the information regarding the aforementioned upper bounds is used for the filtering design. Furthermore, a peak-to-peak performance analysis method is given to achieve the objective of the disturbance attenuation. Unlike in some existing filtering schemes, the information regarding the aforementioned upper bounds is fully utilized in the design for a more relaxed result. Furthermore, on the basis of the proposed peak-to-peak filtering scheme, the influence of the persistent disturbance on the filtering error can be reduced. Finally, two examples are given to demonstrate the validity of the filter scheme presented. (C) 2020 Elsevier B.V. All rights reserved.