A Fuzzy Lyapunov Function Approach for Fault Estimation of T–S Fuzzy Fractional-Order Systems Based on Unknown Input Observer

This article discusses the fault estimation (FE) problem of nonlinear fractional-order (FO) systems subject to faults and unknown inputs through the T–S fuzzy approach. A novel fuzzy FO unknown input observer is well synthesized to not only achieve the desired FE but also decouple the unknown input in contrast to the traditional integer-order observer design technique. It is worth pointing out that the provided FE scheme can reconstruct the fault signal appearing in both input and output equations simultaneously. Furthermore, by resorting to linear matrix inequalities, the stability criteria of observation error dynamics are first formulated based on general quadratic Lyapunov functions, which are further extended via fuzzy Lyapunov functions containing the information of membership functions. Finally, the performance of theoretical results is verified through two elaborate examples.