Analysis of fuzzy observability property for a class of TS fuzzy models

In this paper, the observability property for a class of Nonlinear systems is analyzed under the theoretical framework of Takagi-Sugeno (TS) fuzzy systems. The main contribution of this work is the designing of a full-order TS fuzzy observer, which allows estimating the state vector in a practical way. The analyzed TS fuzzy observer reconstructs the state vector of nonlinear system by using the overall TS fuzzy model represented by the appropriate blending of linear subsystems that operate around certain operation regions. It is considered that at most two membership functions are activated at the same time to facilitate the analysis of the nonlinear system. The proposed approach allows the behavior of the observer to be easily modified by choosing a set of adequate eigenvalues permitting an arbitrary error convergence according to the design requirements. Some numerical simulations are considered to validate the efficacy of the presented approach. Besides, a comparison between the proposed observer and the one settled down under Parallel Distributed Compensation (PDC) concept is given.