Global stabilization of switched nonlinear systems with vanishing control vector fields and its application

Abstract

AbstractThe 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 gk(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.