It is well-known that the non-linear systems transformed into a chained form can not be stabilized by a time-invariant static state feedback control. A lot of approach were proposed to avoid this problem. One of them makes it possible to design a nonlinear control law based on linear control theory by using time-state control form. However, this method needs some input switches and the switching law was not discussed explicitly.
In this paper, at the first, the switching controlled system based on time-state control form is compared with a linear system. We clarify the difference between them and show that influence of switching control is characterized with a certain matrix. Secondly, we propose a periodic switching control law. The necessary and sufficient conditions of stability of the system are shown. At last, we apply the proposed control law to two-wheeled car system and discuss switching period.