Non-Fragile Observer-Based Adaptive Integral Sliding Mode Control for a Class of T-S Fuzzy Descriptor Systems With Unmeasurable Premise Variables - Huang, Xiaorong; Ralescu, Anca L.; Peng, Yiqiang; Gao, Hongli; Sun, Shulei (Frontiers in Neurorobotics, 2022)
The issue of nonfragile observer-based adaptive integral sliding mode control for a class of Takagi-Sugeno (T-S) fuzzy descriptor systems with uncertainties and unmeasurable premise variables is investigated. General nonlinear systems are represented by nonlinear T-S fuzzy descriptor models because the premise variables depend on unmeasurable system states and fuzzy models have different derivative matrices. By introducing the system state derivative as an auxiliary state vector, the original fuzzy descriptor systems are transformed into augmented systems for which the system properties remain the same. First, a novel integral sliding surface, which includes the estimated states of the sliding mode observer and controller gain matrices, is designed to obtain the estimation error dynamics and sliding mode dynamics. Then, some sufficient linear matrix inequality (LMI) conditions for designing the observer and the controller gains are derived by using appropriate fuzzy Lyapunov functions and Lyapunov theory. This approach yields asymptotically stable sliding mode dynamics. The corresponding auxiliary variables are introduced, and Finsler’s lemma is employed to eliminate the coupling of the controller gain matrices, observer gain matrices, Lyapunov function matrices and/or observer gain perturbations. An observer-based integral sliding mode control strategy is obtained to assure that the reachability conditions are satisfied. Moreover, a nonfragile observer and a nonfragile adaptive controller are developed to compensate for system uncertainties and perturbations in both the observer and controller. Finally, example results are presented to illustrate the effectiveness and merits of the proposed method.