This paper applies the state derivative feedback method and proportional plus derivative state feedback method to design the fuzzy controllers for the nonlinear singular systems with external noises. The Takagi-Sugeno fuzzy modeling technology is employed in this paper to represent the nonlinear singular systems with external noise. Considering the singular Takagi-Sugeno fuzzy model, the passivity constraint is chosen to treat the external noises for the controlled systems. By using the parallel distributed compensation method, the fuzzy controller is designed to satisfy the Lyapunov stability conditions and passivity constraints simultaneously. These sufficient conditions can be effectively solved in terms of linear matrix inequalities, which can be solved via the convex optimization technique. At last, some numerical examples are provided to verify the applicability and effectivity of the proposed fuzzy controller design methods.

中文翻译：

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受无源约束的外部噪声非线性奇异系统的模糊控制器设计

本文应用状态微分反馈法和比例加微分状态反馈法设计具有外部噪声的非线性奇异系统的模糊控制器。本文采用Takagi-Sugeno模糊建模技术来表示具有外部噪声的非线性奇异系统。考虑到奇异的 Takagi-Sugeno 模糊模型，选择被动约束来处理受控系统的外部噪声。采用并行分布补偿方法，设计模糊控制器同时满足Lyapunov稳定性条件和无源性约束。这些充分条件可以通过线性矩阵不等式有效求解，可以通过凸优化技术求解。最后，