A strong controllability and observability in linear multivariable control

A particular family of strong controllability and observability properties is shown to be relevant to problems in linear multivariable control. Explicit interrelations are established between these system properties and several approaches to multivariable control: in particular, the abstract vector-space approach of Wonham and Morse, and the explicit algorithm approach of Silverman. The results are valid for systems over an arbitrary field.