On the analysis of feedback systems with a polynomic plant†

Abstract

This paper analyses certain input-output questions of feedback systems whoso open-loop map can be modelled by a polynomic operator, K defined on a Hilbert resolution space. The main objective is to clarify questions of the following type: (1) Given an input, y, is the output, x. well defined? (Existence, Uniqueness) : (2) If x is well defined, what can be said about the mapping y→x? (Causality, Continuity) : (3) Given y, how can x be computed ? (Computational method).