Exact linearization by time scale transformation based on relative degree structure of single-input nonlinear systems

The problem of exact linearization of single-input nonlinear systems by time scale transformation (TST) is considered in this paper. The aim of this paper is to derive method of computing time scale function based on relative degree structure of nonlinear systems. The method using two independent functions which have the largest relative degree of the system is proposed. Because of no requirement of the solution of the nonlinear PDE, the time scale function can be computed easily. An example of the Acrobot is also given. The Acrobot can not be linearized by feedback transformation and state feedback, but this paper shows that the Acrobot is linearizable exactly by applying time scale transformation.