  Dynamic evolution behaviors of dimension-varying control systems often appear
in the genetic regulatory network and the vehicle clutch system etc. An
interesting and significant study on dimension-varying control systems is how
to realize the dimension-varying (the transient dynamics) process smoothly
between the different dimensional subsystems. The quotient space approach is
considered as an effective tool to model the transient dynamics of
dimension-varying control systems.This paper investigates the realization
problem of the transient dynamics of dimension-varying control systems. By
revealing the structure of the controllable subspace for the linear system on
quotient space, we propose the condition for the realization of the transient
dynamics of dimension-varying control systems, based on which a new scheme for
modeling the transient dynamics is given. Moreover, the proposed scheme
justifies the existing result for the strategy for modelling the transient
dynamics. A numeric example is given to illustrate our theoretical results.
