On the Computation of π-Flat Outputs for Linear Time-Delay Systems

2009/10/19 by Morio, Vincent, Cazaurang, Franck, Lévine, Jean
#Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.0910.3619

Abstract

This paper deals with linear time-varying, delay systems. Extensions of the concept of differential flatness \citeFliess₉5 to this context have been first proposed in \citeMounier₉5,Fliess₉6 (see also \citeRudolph₀3,Chyzak₀5), by the introduction of π-flat output. Roughly speaking, it means that every system variable may be expressed as a function of a particular output y, a finite number of its time derivatives, time delays, and predictions, the latter resulting from the prediction operator π^-1. We propose a simple and constructive algorithm for the computation of π-flat outputs based on concepts of polynomial algebra, in particular Smith-Jacobson decomposition of polynomial matrices. Some examples are provided to illustrate the proposed methodology.

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