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Controllability properties and prediction‐free control of linear systems with incommensurate delays
Author(s) -
Gehring Nicole,
Rudolph Joachim,
Woittennek Frank
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110393
Subject(s) - flatness (cosmology) , controllability , linear control systems , control theory (sociology) , ring (chemistry) , property (philosophy) , mathematics , boundary (topology) , linear system , discrete mathematics , control (management) , physics , computer science , mathematical analysis , chemistry , quantum mechanics , organic chemistry , cosmology , epistemology , artificial intelligence , philosophy
For linear delay systems with incommensurate (lumped) delays necessary and sufficient conditions for the freeness of the system over the ring of entire functions in ${\rm I\!\!\!C}(s)[e^{-\tau_1 s},\ldots,e^{-\tau_r s}]$ are given. In contrast to the commensurate case the ring does not have the Bézout property. Therefore, additional criteria are needed involving also special properties of pure delay systems. Based on these results a prediction‐free flatness‐based control is designed for a system of two vibrating strings with a point mass and single boundary input. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)