This article addresses the finite-time boundedness (FTB) problem for nonlinear descriptor systems. Firstly, the nonlinear descriptor system is represented by the Takagi-Sugeno (T-S) model, where fuzzy representation is assumed to be appearing not only in both the state and input matrices but also in the derivative matrix. By using a descriptor redundancy approach, the fuzzy representation in the derivative matrix is reformulated into a linear one. Then, we introduce a fuzzy sliding mode control (FSMC) law, which ensures the finite-time boundedness (FTB) of closed-loop fuzzy control systems over the reaching phase and sliding motion phase. Moreover, by further employing the descriptor redundancy representation, the sufficient condition for designing FSMC law, which ensures the FTB of the closed-loop control systems over the entire finite-time interval, is derived in terms of linear matrix inequalities (LMIs). Finally, a simulation study with control of a photovoltaic (PV) nonlinear system is given to show the effectiveness of the proposed method.

中文翻译：

---

非线性广义系统的有限时间模糊滑模控制

本文解决了非线性描述符系统的有限时间有界（FTB）问题。首先，非线性描述符系统由Takagi-Sugeno（TS）模型表示，其中假定模糊表示不仅出现在状态矩阵和输入矩阵中，而且出现在导数矩阵中。通过使用描述符冗余方法，将导数矩阵中的模糊表示重新公式化为线性表示。然后，我们引入了模糊滑模控制（FSMC）律，该律确保闭环模糊控制系统在到达阶段和滑动运动阶段具有有限时间有界性（FTB）。此外，通过进一步使用描述符冗余表示，为设计FSMC律提供了充分的条件，根据线性矩阵不等式（LMI）推导可确保闭环控制系统在整个有限时间间隔内的FTB。最后，对光伏（PV）非线性系统进行控制的仿真研究表明了该方法的有效性。