Polynomic systems theory: a review

Since publication of a previous review on the subject, the scope and depth of polynomic systems theory has grown considerably. It is the purpose of this paper to explore the subject with as little mathematics as possible in order to clarify the many misconceptions, uses and limitations of the theory. The differences that exist between polynomic systems theory and linear theory, the discrete-time case and the continuous-time case, and the role of polynomic systems as approximations are carefully examined.