Polynomial Observer Design for Time-Delay Polynomial Fuzzy System by Sum of Squares Approach

For polynomial fuzzy system with time delay, this paper presents a new polynomial fuzzy observer design approach via sum of squares approach. We propose an algorithm to design polynomial fuzzy controller and observer satisfying the stability of the overall control system in addition to converging state estimation error to zero. The stability analysis for the augmented systems of the time-delay polynomial fuzzy systems observer-based employ parameter-dependent Lyapunov-Krasovskii functional. All the design conditions in the proposed approach can be represented as sum-of-squares (SOS) problems.