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.
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