In this paper we examine the relationship between control viewed as concatenation of trajectories, and control viewed as interconnection of systems. We show that, for 1D linear time-invariant systems, the ability to obtain a given subsystem by regular interconnection (a prerequisite for any feedback-type structure) is equivalent to the ability to drive any trajectory into that subsystem. However in the case of multidimensional (nD) systems the former is a stronger property than the latter. Trajectory controllability can however be expressed as a regular interconnection of behaviors in an extended variable space, by introducing latent or auxiliary variables. This leads as a by-product to the notion of controlling a system by means of latent variables
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