中文摘要：

针对非线性倒立摆系统，利用小台车平移速度与摆偏角角速度之比，设计了分区的Lyapunov函数和基于自适应律的分段切换控制律。由于该方法考虑了导轨摩擦和节点摩擦对系统的影响，设计的控制律具有较强的鲁棒性，较好地解决了摆的偏角和小车位移非线性强耦合带来的困难，并且得到的是全局渐近稳定的结果。该方法计算简单，且自适应律的应用减少了保守性。最后通过倒立摆实例，利用所设计的控制器进行Matlab仿真，仿真结果验证了所设计控制器的可行性和有效性。

英文摘要：

To the nonlinear inverted pendulum system, the Lyapunov function and the switching controller based on the adaptive law is designed in different parts by using the ratio of the translation speed and the angular velocity of the pendulum angle. The gnideway friction and the node friction are considered for the system, so the designed controller is robust, which can solve the difficulty caused by the strong nonlinear coupling, and the glohle stability can be derived. The calculation is simple, and the adaptive law reduces the system conservative. The Matlab simulation on the inverted pendulum example shows that the conclusion is feasible and effective.