非Lipschitz连续级联系统的稳定性分析及其应用

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.

Stability of non-Lipschitz continuous cascaded systems and its application

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.