A Sum of Squares Approach for Polynomial Fuzzy Observer Design for Polynomial Fuzzy Systems with Unknown Inputs

This paper investigates the problem of designing an unknown inputs observer to estimate states of a class of nonlinear systems that can be modeled by polynomial fuzzy systems subject to unknown inputs. The proposed method provides important innovations over the existing unknown inputs observers since the designed observer has a polynomial fuzzy structure. Based on the Lyapunov approach, the proposed observer is developed to guarantee the asymptotic stability of the estimation error and sufficient design conditions are given in Sum Of Squares formulations with equality constraints. Both continuous-time and discrete-time cases are addressed and relaxed conditions are also introduced by using intermediate variables that can be easily solved via numerical tools. Finally, an illustrative example is given to provide the effectiveness of the proposed methodology.