The lattice structure of behaviors (Q2719142)

The author explains the algebraic structure of the set of all linear (distributed) behaviors. This paper argues that the relevant structure is a modular lattice.NEWLINENEWLINENEWLINEIn the first section the author describes the calculus of Willems submodules. The description of the lattice structure is based on the corollary, that in classical spaces, the Willems closure of a finite intersection equals the intersection of the individual Willems closures. NEWLINENEWLINENEWLINEIn the next section the structure of behaviors is investigated. The author shows that the lattice of all behaviors in a classical space is a modular lattice. The final section concerns the structure of stable and stabilizable behaviors.