Observer Designs for a General Class of Takagi-Sugeno Fuzzy System with Unmeasurable Premise Variables

We propose approaches regarding observer designs for nonlinear systems represented by Takagi-Sugeno fuzzy model in the case that premise variables are unmeasurable. In the framework of Takagi-Sugeno fuzzy system, an observer problem is one of the big challenging tasks because appropriate error closed-loop system is not easily established due to a mismatch problem caused by the unmeasurable premise variables. In the literatures, such a difficulty is limited to the use of a linear output equation. However, in this paper, we show our proposed approach can also handle a nonlinear output equation. Our approach utilizes the differential mean value theorem and this allows to establish a suitable error closed-loop system even with output equations having nonlinearities. The transformed suitable error closed-loop holds convex sum property. Therefore, the stability conditions for the error closed-loop system is obtained in terms of linear matrix inequalities (LMIs) via Lyapunov stability theorem. Finally, a numerical example is provided to show that the main result work properly.