On Multi Time-Scale Form of Nonlinear Systems

In general, controller is designed with respect to one time scale. Time-state control form divides a system into virtual time control part and state control part, and the system is linearized based on two time scales; real and virtual time scales. This paper claims that handling of time scales for a control system should be more flexible, and introduces a multi time-scale transformation as a generalization of time scale transformation. As an example, a mechanical system is linearized under two virtual time scales.