非Lipschitz连续级联系统的稳定性分析及其应用(英文)

Stability of non-Lipschitz continuous cascaded systems and its application

中文关键词  级联系统  积分输入到状态稳定  有限时间控制  齐次性

英文关键词  cascaded system  iISS  finite-time control  homogeneity

中文摘要

      当考虑级联系统稳定性时, 一般都需要系统满足局部或者全局Lipschitz连续性条件. 与已有文献中的结果不同, 本文给出了一种处理满足非Lipschitz连续条件下级联系统的稳定性分析方法. 首先, 基于积分输入状态稳定的定义, 给出了级联系统全局稳定的Lyapunov形式条件. 基于此, 继续讨论了非Lipschitz连续情况下级联系统的有限时间稳定性. 然后, 利用上述稳定性分析结果, 讨论了一类驱动子系统具有上三角结构的级联系统的控制设计问题. 最后, 给出几个例子验证了上述结果的有效性.

英文摘要

      The local/global Lipschitz continuity is always required when considering the stability of the cascaded systems. Being different from the exiting methods proposed in the literature, we give a method to handle the non-Lipschitz continuous cascaded systems. By using the definition of iISS (integral input-to-state stability), the Lyapunov-like conditions for global stability of non-Lipschitz continuous cascaded systems are derived. Then, based on this, the finite-time stability for non-Lipschitz continuous cascaded systems is further studied. The stability analysis results are applied to the control design problem for a class of cascaded systems with upper-triangular deriving subsystem. Finally, some examples are proposed to validate the effectiveness of the proposed results.