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利用Filippov解、Clarke广义梯度和非光滑Lyapunov稳定理论,对一类滑模面设计为非光滑线性Lipschitz连续平面的二阶系统滑模控制问题进行深入讨论.首先设计控制律,使闭环系统在有限时间内能够到达所设计的滑模面;然后证明系统在滑模面上的运动是渐近稳定的.放宽了对滑模控制中滑模面设计的要求,提高了所提出设计方法的灵活性,有利于改善系统性能.仿真结果验证了所提出设计方法的正确性和有效性.
In this paper, a class of sliding mode control problems for a class of second-order systems with non-smooth linear Lipschitzian continuous surfaces is discussed by using the Filippov solution, Clarke’s generalized gradient and the non-smooth Lyapunov stability theory.Firstly, the control law is designed to make the closed- Time can reach the designed sliding surface, and then the system is proved to be asymptotically stable on the sliding surface, which relaxes the design of sliding surface in sliding mode control and improves the flexibility of the proposed design method , Which is helpful to improve the system performance.The simulation results verify the correctness and effectiveness of the proposed design method.