CONTROLLABILITY AS MINIMALITY

摘要

Among many other things, Oberst proved in his fundamental paper that controllabilityis equivalent to minimality in a transfer equivalence class. In this paper we directly and explicitly describe minimal systems in terms of transfer functions. A transfer function is a purelyalgebraic object that is associated to a linear differential system and that determines in an explicitform a certain “trivial” part of the system. Trajectories belonging to this part are called transfertrajectories. It is shown that a linear differential system is controllable if and only if every one of its trajectories can be obtained from a transfer trajectory by using a finite number of differentiations.