The global stabilization problem for a more extensive class of switched nonlinear systems is studied, in which control vector fields are allowed to vanish at some point, even for all the subsystems at the same time. The main work of this article is to design a control vector fields-dependent switching law and a bounded switching controller to stabilize the switched nonlinear systems. First, a sufficient condition ensuring the global stabilization of such a class of switched nonlinear systems is developed by the dual design of controllers and a switching law. In some special cases, the designed switching law can rule out Zeno behavior. Then, as a verification of the proposed control design method, the global stabilization of switched strict-feedback nonlinear systems with g_k(x) vanishing at some points is obtained by the codesign of the control vector fields-dependent switching law and the bounded switching controller. Finally, a switched RCL circuit system example is also provided to demonstrate the effectiveness of the developed method.

中文翻译：

---

具有消失控制向量场的切换非线性系统的全局镇定及其应用

研究了更广泛的一类切换非线性系统的全局稳定问题，其中允许控制向量场在某个点消失，甚至所有子系统同时消失。本文的主要工作是设计控制向量场相关切换律和有界切换控制器来稳定切换非线性系统。首先，通过控制器和切换律的双重设计，开发了确保此类切换非线性系统全局稳定的充分条件。在某些特殊情况下，设计的开关定律可以排除 Zeno 行为。然后，作为对所提出的控制设计方法的验证，具有g _k ( x) 在某些点消失是通过控制向量场相关切换律和有界切换控制器的共同设计获得的。最后，还提供了一个开关 RCL 电路系统示例，以证明所开发方法的有效性。