Discrete-time polynomial fuzzy observer designs via a sum of squares approach

In this paper, a sum of squares(SOS) method is proposed to design observers for discrete-time polynomial fuzzy systems. The proposed SOS approach has two improved and innovative results for the existing linear matrix inequality (LMI) method to Takagi-Sugeno(T-S) discrete fuzzy observer designs. Firstly, a polynomial discrete fuzzy model is developed, which is a generation of the well-known T-S fuzzy system. Secondly, the conditions in the proposed approach are obtained in terms of SOS, which is the extension of the LMI method. Therefore, the conditions given in this paper are more general than the existing LMI approaches to T-S fuzzy systems. An example is given to show the effectiveness, which also demonstrate the SOS approaches are more relaxed than the existing LMI approaches. Finally, a conclusion is given to complete the paper.