Realisation of the transient dynamics of dimension-varying control systems

The quotient space method provides a novel idea for modelling the transient dynamics of dimension-varying control systems. This paper investigates the realisation 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 realisation of the transient dynamics of dimension-varying control systems, based on which a new scheme for modelling 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.