Volume 26, 2020
|Number of page(s)||34|
|Published online||10 September 2020|
Multiplicity-induced-dominancy in parametric second-order delay differential equations: Analysis and application in control design*
Inria Saclay, DISCO team & L2S, Université Paris Saclay, CNRS-CentraleSupélec-Université Paris Sud, 3 rue Joliot-Curie, 91192 Gif-sur-Yvette cedex, France & DRII-IPSA, Bis,
63 Boulevard de Brandebourg,
2 L2S, Université Paris Saclay, CNRS-CentraleSupélec-Université Paris Sud, 3 rue Joliot-Curie, 91192 Gif-sur-Yvette cedex, France & Inria Saclay, DISCO team.
3 DRII-IPSA, Bis, 63 Boulevard de Brandebourg, 94200 Ivry-sur-Seine France.
** Corresponding author: firstname.lastname@example.org
Accepted: 23 November 2019
This work revisits recent results on maximal multiplicity induced-dominancy for spectral values in reduced-order time-delay systems and extends it to the general class of second-order retarded differential equations. A parametric multiplicity-induced-dominancy property is characterized, allowing to a delayed stabilizing design with reduced complexity. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates’ delays and gains result from the manifold defining the maximal multiplicity of a real spectral value, then, the dominancy is shown using the argument principle. Sensitivity of the control design with respect to the parameters uncertainties/variation is discussed. Various reduced order examples illustrate the applicative perspectives of the approach.
Mathematics Subject Classification: 4C60 / 34K06 / 35B35 / 70J25
Key words: Time-delay systems / stability and stabilization / exponential decay / pole-placement / control design
© EDP Sciences, SMAI 2020
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