中文摘要：

双轮小车的平衡与稳定受到执行器饱和问题的困扰。将小车的稳定问题转化成一个标准的控制问题，对小车建立非线性数学模型，并研究在状态反馈条件下自适应容错控制器的设计问题。利用线性矩阵不等式的方法进行处理，给出固定增益和自适应控制算法的设计方法。利用MAT．LAB对系统进行仿真并分析最终结果，得出一种能够使系统更加稳定的算法。

英文摘要：

The balance and stability of the two-wheeled trolley are plagued by the problem of actuator satu- ration. To establish its nonlinear mathematical model, the stability of the trolley can be transformed into a standard control, and the design of self-adaptive fault-tolerant controllers will be studied under the state feed- back condition, which will be dealt with by using the LMI to work out a design method about fixed gain control algorithm and self-adaptive control algorithm. The analysis of the final result by using the MATLAB simulation can come up with an algorithm which may make the system more stable.