Trajectory Control and Interconnection of 1D and nD Systems

Abstract

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 one-dimensional 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 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.