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

By Islam Boussaada, Silviu-Iulian Niculescu, Ali El-Ati, R. Pérez-Ramos, Karim Trabelsi. E S A I M: Control, Optimisation and Calculus of Variations, 2020

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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.

Subfields: Applied Mathematics, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/17eacd1e119f484396a0fdf7a35fe6aa4debc189

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Citations in the corpus

Multiplicity-induced-dominancy for delay-differential equations of retarded type (2020, methodology): “The strategy of our proof of Theorem 3.1 starts by a suitable classical change of variables allowing to treat only the case s 0 = 0 and τ = 1 (see, for instance, [10]).”