Abstract
The cross-dimensional linear control systems, both discrete time and continuous time cases are investigated. Only time-invariant case is considered. In discrete time case, since the calculation of trajectory is straightforward, we consider its controllability and observability. As for continuous time case, we mainly focus on the modeling of the problem and provide the expressions of the corresponding trajectories. The cross-dimensional linear (control) systems on quotient space are also considered. Finally, the finite dimensional projective realization of dimension unbounded cross-dimensional systems is discussed.
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