Sliding-Mode Control of Fuzzy Singularly Perturbed Descriptor Systems

Due to the complicated model characteristics, only a few results focusing on stability analysis have appeared on singularly perturbed descriptor systems (SPDSs). This article instead proposes an integral sliding-mode control strategy for a kind of Takagi-Sugeno fuzzy approximation-based nonlinear SPDSs under time-varying nonlinear perturbation. An appropriate fuzzy integral switching manifold that fully accommodates the system features is designed to completely reject the matched perturbation without amplifying the unmatched one. To facilitate the synthesis of the high-level controller (HLC), the sliding-mode dynamics (SMD) is transformed into an augmented form. Thanks to the adoptions of a novel singular perturbation Lyapunov function, Finsler's lemma, as well as the fixed-point principle, the existence and uniqueness of the solution and the exponential admissibility for the augmented SMD are analyzed. A solution for the designed HLC is further provided. To guarantee the sliding motion, a fuzzy integral sliding-mode controller (FISMC) is synthesized by analyzing the sliding motion reachability. An adaptive FISMC is also given to deal with the unknown upper bounds of the matched perturbation. Finally, the applicability of the developed FISMC strategy is testified by a practical example.