This paper investigates observer-based stabilization for nonlinear descriptor systems using a fuzzy integral sliding mode control approach. Observer-based integral sliding mode control strategies for the Takagi-Sugeno (T-S) fuzzy descriptor systems are developed. A two-step design approach is first developed to obtain the observer gains and coefficients in the switching function using linear matrix inequalities (LMIs), and the results are used to facilitate the development of a single-step design approach, which is seen to be convenient but introduces some conservatism in the design. The potential application to a class of mechanical systems is also considered. Since the descriptor system representation of mechanical systems is adopted, it is shown that in contrast to the existing fuzzy sliding mode control methods based on the normal system representation, the resulting T-S fuzzy system does not contain different input matrices for each local subsystem and the required number of fuzzy rules is consequently markedly reduced. Finally, the balancing problem of a pendulum on a car is numerically simulated to demonstrate the effectiveness of the proposed method.

中文翻译：

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非线性描述系统的基于观测器的模糊积分滑模控制


本文使用模糊积分滑模控制方法研究了非线性描述符系统的基于观测器的稳定性。开发了用于 Takagi-Sugeno (TS) 模糊描述符系统的基于观测器的积分滑模控制策略。首先开发了一种两步设计方法，以使用线性矩阵不等式（LMI）获得切换函数中的观测器增益和系数，并将结果用于促进单步设计方法的开发，这被视为方便，但在设计上引入了一些保守主义。还考虑了一类机械系统的潜在应用。由于采用了机械系统的描述符系统表示，结果表明，与现有的基于普通系统表示的模糊滑模控制方法相比，所得到的TS模糊系统不包含每个局部子系统的不同输入矩阵以及所需的输入矩阵。模糊规则的数量因此显着减少。最后，对汽车摆锤的平衡问题进行了数值模拟，证明了该方法的有效性。