Polynomial Embedding Algorithms for Controllers in a Behavioral Framework

In this correspondence, we will establish polynomial algorithms for computation of controllers in the behavioral approach to control, in particular for the computation of controllers that regularly implement a given desired behavior and for controllers that achieve pole placement and stabilization by behavioral full interconnection and partial interconnection. These synthesis problems were studied before in articles by Belur and Trentelman, Rocha and Wood, and Willems in the reference section. In the algorithms, we will apply ideas around the unimodular and stable embedding problems. The algorithms that are presented in this correspondence can be implemented by means of the Polynomial Toolbox of Matlab.