In this paper, the problem of stabilization with optimal L1-gain for positive T-S fuzzy systems is investigated with the use of linear Lyapunov function. A T-S fuzzy model for positive nonlinear system is established to study the stabilization control for the positive system. Sufficient condition for stabilization is presented in term of linear programming. The static output-feedback fuzzy controller is constructed to guarantee that the closed-loop system is controlled positive, asymptotically stable and the L1-gains from the exogenous inputs to the regulated output is minimized, respectively. Moreover, the stabilization problem with optimal L∞-gain for positive T-S fuzzy systems is solved. Finally, three examples are presented to show the effectiveness of the theoretical results.

中文翻译：

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正 TS 模糊系统的最优 L1-Gain 和 L∞-Gain 稳定控制

在本文中，具有最优 L 的稳定问题1使用线性 Lyapunov 函数研究了正 TS 模糊系统的增益。建立正非线性系统的TS模糊模型，研究正系统的镇定控制。以线性规划的形式给出了稳定的充分条件。构造了静态输出反馈模糊控制器，以保证闭环系统被控制为正、渐近稳定和L1- 从外生输入到调节输出的增益分别最小化。此外，具有最优 L 的稳定问题∞- 正 TS 模糊系统的增益得到解决。最后通过三个例子说明了理论结果的有效性。