Output tracking: an application for irrational SISO transfer functions and a survey for MIMO systems

Abstract

In this paper we consider (MIMO) finite dimensional linear and time-invariant systems and irrational single-input single-output (SISO) transfer functions. In both cases our aim is to describe as best as possible the range of the input-output map $u(\cdot )\mapsto y(\cdot )$. The theory in finite dimension is quite satisfying but rather scarce, the first aim of this paper is to collect the main results in this direction in a comprehensive way. Our second aim is to improve a recent result on the tracking problem for irrational SISO transfer functions, allowing one to completely describe the outputs of such system for inputs $u\in L^2(0,\infty )$. An application is given for a heat equation with polynomial coefficients.