This article presents a new approach to design static output-feedback (SOF) controllers for constrained Takagi-Sugeno fuzzy systems with nonlinear consequents. The proposed SOF fuzzy control framework is established via the absolute stability theory with appropriate sector-bounded properties of the local state and input nonlinearities. Moreover, both state and input constraints are explicitly taken into account in the control design using set-invariance arguments. Especially, we include the local sector-bounded nonlinearities of the fuzzy systems in the construction of both the nonlinear controller and the nonquadratic Lyapunov function. Within the considered local control context, the new class of nonquadratic Lyapunov functions provides an effective solution to estimate the closed-loop domain of attraction, which can be nonconvex and even disconnected. The convexification procedure is performed using specific congruence transformations in accordance with the special structures of the proposed SOF controllers and nonquadratic Lyapunov functions. Consequently, the fuzzy SOF control design can be reformulated as an optimization problem under strict linear matrix inequality constraints with a linear search parameter. Compared to existing fuzzy SOF control schemes, the new structures of the control law and the Lyapunov function are more general and offer additional degrees of freedom for the control design. Both theoretical arguments and numerical illustrations are provided to demonstrate the effectiveness of the proposed approach in reducing the design conservatism.

中文翻译：

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具有受状态和输入约束的局部非线性模型的离散时间模糊系统的约束输出反馈控制


本文提出了一种为具有非线性结果的约束 Takagi-Sugeno 模糊系统设计静态输出反馈 (SOF) 控制器的新方法。所提出的 SOF 模糊控制框架是通过绝对稳定性理论建立的，具有适当的局部状态和输入非线性的扇区边界属性。此外，在使用集合不变性参数的控制设计中明确考虑了状态和输入约束。特别是，我们在非线性控制器和非二次 Lyapunov 函数的构造中包含了模糊系统的局部扇区有界非线性。在考虑的局部控制背景下，新型非二次李雅普诺夫函数提供了一种有效的解决方案来估计闭环吸引域，该闭环吸引域可以是非凸的，甚至可以是断开的。根据所提出的 SOF 控制器和非二次 Lyapunov 函数的特殊结构，使用特定的同余变换来执行凸化过程。因此，模糊 SOF 控制设计可以在具有线性搜索参数的严格线性矩阵不等式约束下重新表述为优化问题。与现有的模糊SOF控制方案相比，控制律和Lyapunov函数的新结构更加通用，并为控制设计提供了额外的自由度。提供了理论论证和数值说明来证明所提出的方法在减少设计保守性方面的有效性。