Unknown Input-Based Observer Synthesis for a Polynomial T–S Fuzzy Model System With Uncertainties

This paper proposes a new approach based on the unknown input method to synthesize the observer for polynomial Takagi–Sugeno fuzzy system with uncertainties. In this paper, the upper bounds of uncertainties are not given and the effect of uncertainties is eliminated without designing an extra controller. With the aids of the noncommon Lyapunov theory and Matlab's tools of the sum-of-square, a new observer is synthesized in which the observer form is completely different from the traditional observer forms reported in previous papers. The conditions for the observer synthesis are much relaxed and the complexity of the design process is reduced. Finally, two illustrative examples are presented to demonstrate the effectiveness of the proposed method.