Switching control of chained systems based on time-state control form

It is well-known that the non-linear systems transformed into chained form can not be stabilized by a time-invariant static state feedback control. That is why many approaches have been proposed to avoid this problem. One of them makes it possible to design a nonlinear control law based on the linear control theory by using time-state control form. However, this method needs some input switches and the switching law has not been discussed explicitly. In this paper, the switching controlled system based on time-state control form is represented as a piecewise linear system. It is verified that the influence of switching control is characterized by a certain matrix. Then, we propose a periodic switching control law The necessary and sufficient conditions for stabilizing the system are obtained. The proposed control method is applied to two examples and the switching periods are discussed.