Based on the integral inequality and other quality proved, the paper discusses the conclusion of the mid-value in theorem of integration mean which is got in open interval.

在证明了定积分不等式等性质的基础上，给出并证明了积分中值定理的中值在开区间内取得的结论。

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Then, a new sufficient condition for the stability of open-loop system is proposed based on linear matrix inequality (LMI); and a fuzzy controller is designed via non-quadratic PDC control law.

然后，基于一系列线性矩阵不等式，得到了开环系统稳定的充分条件，进而又基于非二次PD C控制律，设计出了模糊控制器。

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Then, a new sufficient condition for the stability of open-loop system is proposed based on linear matrix inequality (LMI); and a fuzzy controller is designed via non-quadratic PDC control law.

然后，基于一系列线性矩阵不等式，得到了开环系统稳定的充分条件，进而又基于非二次PD C控制律，设计出了模糊控制器。

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