Relaxed Observer-Based State Estimation of Discrete-Time Takagi–Sugeno Fuzzy Systems Based on an Augmented Matrix Approach

In this paper, relaxed observer-based state estimation of discrete-time Takagi–Sugeno fuzzy systems is proposed via developing a new augmented matrix approach. In contrast with the recent method reported in the literature, a more advanced introduction mode of additional matrices is developed without any redundant constraint under the framework of homogeneous polynomials. Then, the proposed augmented matrices can be built in order to depict the characteristic information of each possible working mode in a superior way, and thus our obtained result is less conservative than the recent one. Moreover, it is worth noting that that the recent method belongs to the special case of ours. Finally, two numerical simulations are given to test and validate the superiority and generality of the developed method.