Abstract
A dimension-free state space is proposed, which is equipped with a cross-dimensional distance. This distance leads to projections over Euclidean spaces of different dimensions and the corresponding linear systems on them. Based on these projections, equivalences of vectors and matrices of different dimensions are proposed, and dynamics on quotient space is obtained. Finally, using lifts of dynamic systems on quotient space to Euclidean spaces of different dimensions, a cross-dimensional model is proposed to deal with the dynamics of dimension-varying process of linear systems. As an application, the control of clutch system is investigated.
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