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The lattice structure of behaviors. (English) Zbl 0983.93025
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.
In 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.
In 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.

93C20 Control/observation systems governed by partial differential equations
93C35 Multivariable systems, multidimensional control systems
35B37 PDE in connection with control problems (MSC2000)
35E20 General theory of PDEs and systems of PDEs with constant coefficients
06C05 Modular lattices, Desarguesian lattices
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