中文摘要：

针对参数不确定平面运动n级倒立摆系统,研究了鲁棒保成本模糊控制器设计问题。给出了将系统动力学模型转化为一种新型广义T-S模糊模型的方法,由此避免了求逆矩阵的过程。为获得保守性更低的系统稳定性设计条件,通过引入松弛变量矩阵来解耦Lyapunov函数中的系统矩阵,增加了设计条件的自由度。然后讨论了最优鲁棒保成本模糊控制器的设计条件,并将这些条件转换成了线性矩阵不等式（LMI）的凸优化问题。最后,在仿真实验中以平面运动二级倒立摆系统为例验证了本文方法的有效性。

英文摘要：

For a class of planar n-order inverted pendulums（PnIP） with parameter uncertainties, Design strategy of robust guaranteed cost fuzzy controller is discussed. Firstly, a new method which transform dynamic model of PnlP into a new-type fuzzy descriptor system is proposed, which avoids the complexities of matrix inversion. In order to reduce the conservativeness in stability analysis of fuzzy control systems, slack matrix variables are introduced to decouple the Lyapunov matrices from the system matrices, which provides extra degrees of freedom to the stability conditions. Then, the design conditions of optimal robust guaranteed cost fuzzy controller are obtained, and these are changed into a convex optimization problem in terms of linear matrix inequalities （LMI）. Finally, a numerical example for planar double inverted pendulums is given to illustrate the effectiveness of the proposed approach.