Adaptive Sliding Mode Observer Design for a Class of T–S Fuzzy Descriptor Fractional Order Systems

This paper investigates the problem of sliding mode observer (SMO) design for Takagi-Sugeno (T-S) fuzzy descriptor fractional order systems (FOSs) with fractional order $0<; \alpha <; 1$. First, an SMO is designed for the T-S fuzzy descriptor FOS. Then, a fuzzy fractional order integral-type sliding surface is constructed. By utilizing the fuzzy sliding surface, the assumption that all local input matrices are identical in most existing results about sliding mode control (SMC) for T-S fuzzy systems, can be removed. Then, a new sufficient condition is proposed in terms of linear matrix inequalities (LMIs), which guarantees the admissibility of the sliding mode dynamics. Moreover, adaptive SMC strategy is used such that the reachability condition can be guaranteed. Finally, three examples are given to verify the effectiveness of our results.