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针对一类二阶不确定系统,构造了以线性Lipschitz曲面作为边界的自稳定域,并依此设计控制律,利用Filippov解与空间非光滑曲面的相依锥判据,证明在该控制律的作用下系统轨迹将在有限时间到达所设计的自稳定域边界并进入其内部,从而系统轨迹将收敛到原点.所得结果放宽了对自稳定域边界光滑性的要求,提高了设计的灵活性.仿真结果验证了设计的正确性和有效性.
For a class of second-order uncertain systems, a self-stable region with a linear Lipschitz surface as a boundary is constructed. Based on this, a control law is designed. By using the conic cone criteria of Filippov solutions and non-smooth surfaces, The trajectory of the lower system will reach the designed boundary of the self-stability domain and enter its interior in a limited time, so that the system trajectory will converge to the origin. The obtained results relax the requirements for the smoothness of the boundary of the self-stability domain and improve the flexibility of the design. The results verify the correctness and validity of the design.