Equivalence‐based controllability of dimension‐varying systems on quotient space

Abstract

AbstractThe quotient space approach is considered as an effective and pioneering tool to model the transient dynamics of dimension‐varying systems recently. In this paper, we focus on the controllability of dimension‐varying systems that are modeled by the quotient space approach. First, we investigate the relation of controllability matrix between so‐called equivalent lifting systems. The result of the investigation prompts us to propose a new concept called equivalent class controllability for dimension‐varying systems on quotient space. Moreover, the coordinate transformation of states on quotient space is studied. Based on it, the controllable normal form of dimension‐varying systems on quotient space, which follows the criterion for the equivalent class controllability, is presented.