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

Boussaada, Islam; Niculescu, Silviu-Iulian; El-Ati, Ali; Pérez-Ramos, Redamy; Trabelsi, Karim

ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 57.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

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.

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