A fuzzy integral sliding-mode parallel control approach for nonlinear descriptor systems

This paper considers the stabilization problem of nonlinear descriptor systems through Takagi–Sugeno (T-S) fuzzy models of type 1. A novel fuzzy integral sliding mode parallel control strategy is proposed, where the T-S fuzzy model is employed to equivalently approximate any nonlinear descriptor system. A fuzzy sliding-mode parallel controller is constructed to robustly control the T-S fuzzy model and, consequently, to semi-globally stabilize the corresponding nonlinear descriptor system. The developed control scheme can remove a restrictive assumption on the system input channel and is applicable to general nonlinear descriptor systems. Moreover, universality discussion of the developed controller for two kinds of nonlinear descriptor systems is provided, which endows the proposed method with more confidence in real industrial applications. Finally, two examples numerically demonstrate the feasibility and advantages of the developed controller.