Enhanced gain‐scheduling fault estimation of discrete‐time Takagi–Sugeno nonlinear systems: A novel free matrix approach

A novel gain‐scheduling fault estimation is developed on the direction of improving algorithm efficiency based on discrete‐time Takagi–Sugeno fuzzy models. Different from the traditional results in which the zero‐order free matrices are applied, a novel free matrix approach is proposed and the higher‐order free matrices are for the first time introduced in designing conditions of the fuzzy gain‐scheduling fault estimation observer. For each working mode, its proprietary properties about current‐time normalized fuzzy weighting functions are made full use and thus the anti‐interference ability of the developed fuzzy gain‐scheduling fault estimation observer is enhanced without any increase of either the consumed time of solving the required designing criterion or the number of gain scalars needed to be stored in random access memory of the computer in real time. It does provide a good chance to obtain equal or better results of fuzzy gain‐scheduling fault estimation with the usage of much less computing resource than before, which is much meaningful to the applications of theoretical methods. Finally, the effectiveness and superiority of our developed free matrix approach are tested and validated by using performance comparisons on the benchmark example.