Neural Network Based Adaptive SMO design for T-S Fuzzy Descriptor Systems

This article is concerned with the problem of sliding-mode observer (SMO) design for Takagi–Sugeno (T–S) fuzzy descriptor systems with time-varying delay. First, based on the restricted equivalent transformation, a new restricted equivalent form (REF) of descriptor systems is proposed. Under the new REF, an integral-type sliding surface is constructed for the error system. Then, a sufficient condition is established in terms of linear matrix inequality, which guarantees the admissibility of the sliding-mode dynamics. Furthermore, an radial basis function (RBF) neural network based adaptive sliding-mode control (SMC) strategy is adopted such that the reachability condition can be ensured. By utilizing the RBF neural network to approximate the unknown nonlinearity, many restricted conditions, which are required in most existing results about SMC for T–S fuzzy systems, can be removed. Finally, simulation examples are presented to show the effectiveness of our results.