Abstract This paper is concerned with the problem of sliding mode observer design and observer-based sliding mode controller synthesis for polynomial fuzzy singular systems with time-delay. The polynomial fuzzy model is constructed for singular nonlinear system to eliminate the upper and lower bounds restriction of states in the system and reduce the calculation quantity. An integral-type sliding surface function, which has a stabilizing effect on the sliding variable, is proposed for the observer system. In terms of sum-of-squares approach, observer-based sliding mode passive controller is designed for the system with unknown membership functions, which drives the system trajectories onto the predefined sliding surface in a finite time, meanwhile, the stability and robust passivity of the closed-loop system are guaranteed. The information of membership functions is included in the stability conditions, which can reduce the conservatism. Finally, an example is performed to verify the merits of the method proposed.

中文翻译：

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基于观测器的滑模控制时滞多项式模糊奇异系统的被动控制

摘要 本文研究具有时滞多项式模糊奇异系统的滑模观测器设计和基于观测器的滑模控制器综合问题。针对奇异非线性系统构建多项式模糊模型，消除系统状态的上下界限制，减少计算量。针对观测器系统提出了一种对滑动变量具有稳定作用的积分型滑动面函数。在平方和方法方面，针对隶属函数未知的系统设计了基于观测器的滑模被动控制器，在有限的时间内将系统轨迹驱动到预先定义的滑动面上，同时保证了系统的稳定性和鲁棒性。保证闭环系统。稳定性条件中包含隶属函数信息，可以降低保守性。最后，通过一个例子来验证所提出方法的优点。