# Realization of the transient dynamics of dimension-varying control systems

## TL;DR

This paper addresses how to smoothly realize the transient dynamics in dimension-varying control systems using quotient space modeling, providing conditions and schemes for effective realization.

## Contribution

It introduces a new scheme for modeling transient dynamics in dimension-varying control systems based on quotient space analysis, extending existing strategies.

## Key findings

- Established controllable subspace structure on quotient space
- Proposed conditions for realizing transient dynamics
- Validated scheme with a numerical example

## Abstract

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.