Multiplicity-induced-dominancy in parametric second-order delay differential equations: Analysis and application in control design^*

¹ 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, 94200 Ivry-sur-Seine France.
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: islam.boussaada@gmail.com

Received: 24 June 2019
Accepted: 23 November 2019

Abstract

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.