Summary: Appropriate modeling for a controlled plant has been a remarkable problem in the control field. A new modeling theory, i.e. characteristic modeling, is roundly demonstrated. It is deduced in detail that a general linear constant high-order system can be equivalently described with a two-order time-varying difference equation. The application of the characteristic modeling method to the control of flexible structure is also introduced. Especially, as an example, the Hubble Space Telescope is used to illustrate the application of the characteristic modeling and adaptive control method proposed in this paper.