Unknown Input Observer Designs for Polynomial Fuzzy Systems with Uncertainties

This study developed a novel design framework for unknown input observers in uncertain polynomial fuzzy systems using the sum-of-squares algorithm. First, both the system and the input matrices depended on unmeasurable state variables that required estimation. Secondly, the observer structure in this study differed from existing formulations. The proposed observer eliminated uncertainty effects without requiring explicit bounds or auxiliary controllers. The incorporation of slack matrices facilitated the resolution of non-convex terms in the stability conditions, thereby reducing design conservatism. Finally, a simulation study was conducted, and the results confirmed the validity and theoretical value of the developed strategy.