A study of behaviors
In this long article the author presents a personal account of the behavioral system theory developed by J. C. Willems in terms of polynomial and rational models. The principal new results concern the introduction and the characterization of the notion of behavior homomorphisms and their application to a unified derivation of equivalence results for different classes of behavioral representations. Starting from the fact that rational models can be seen as a class of autonomous behaviors, the polynomial model approach is extended to behaviors and several representations of behavioral systems are shown to be equivalent. The notion of behavior controllability introduced by J. C. Willems is thoroughly investigated and compared with the notion of reachability in the behavioral setting. The paper gives a self-contained description of the proposed approach, since the fundamental results of the polynomial model approach to linear systems are recalled as well as the basic facts of the behavior theory. A large number of known results concerning different representations of behaviors and their properties are presented in a coherent and compact form, and a rich bibliography is provided.
scientific article; zbMATH DE number 1790285
scientific article