Output tracking: an application for irrational SISO transfer functions and a survey for MIMO systems
Lucas Davron
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(·) y(·). 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 ∈ L2(0,∞). An application is given for a heat equation with polynomial coefficients.
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