Editing Controllability (section)

== Controllability in the behavioral framework ==

In the so-called [[behavioral system theoretic approach]] due to Willems (see [[people in systems and control]]), models considered do not directly define an input&ndash;output structure. In this framework systems are described by admissible trajectories of a collection of variables, some of which might be interpreted as inputs or outputs.

A system is then defined to be controllable in this setting, if any past part of a behavior (trajectory of the external variables) can be concatenated with any future trajectory of the behavior in such a way that the concatenation is contained in the behavior, i.e. is part of the admissible system behavior.<ref name="Polderman98">{{cite book|author1=Jan Polderman |author2=Jan Willems |title=Introduction to Mathematical Systems Theory: A Behavioral Approach|edition=1st|year=1998|publisher=Springer Verlag|location=New York|isbn=978-0-387-98266-3}}</ref>{{rp|151}}