Abstract
The control method based on the Time-state control form makes it easy to apply the linear control theory into the controller design of chained systems. However, this control method requires the switches of the control inputs. Therefore, we have to discuss the stabilization conditions for the switched system. The sufficient conditions for stabilization have been previously formulated as the condition for the existence of a common Lyapunov function. In this paper, a common Lyapunov function for the switched system is shown explicitly. On the basis of the function, it is clarified that the stabilization conditions for the switched system are equal to those for a basic continuous-time linear system.
