Effects of Roots of Maximal Multiplicity on the Stability of Some Classes of Delay Differential-Algebraic Systems: The Lossless Propagation Case

Guilherme Mazanti (1, 2) , Islam Boussaada (1, 2) , Silviu-Iulian Niculescu (3, 2) , Yacine Chitour (3)

1 IPSA - Institut Polytechnique des Sciences Avancées
2 DISCO - Dynamical Interconnected Systems in COmplex Environments
3 L2S - Laboratoire des signaux et systèmes

It has been observed in several recent works that, for some classes of linear time-delay systems, spectral values of maximal multiplicity are dominant, a property known as multiplicity-induced-dominancy (MID). This paper starts the investigation of whether MID holds for delay differential-algebraic systems by considering a single-delay system composed of two scalar equations. After motivating this problem and recalling some recent results for retarded delay differential equations, we prove that the MID property holds for the delay differential-algebraic system of interest and present some applications.

Mots clés: time-delay equations; stability analysis; spectral methods; root assignment

Domaines: Automatique / Robotique; Systèmes dynamiques [math.DS]; Optimisation et contrôle [math.OC]; Equations aux dérivées partielles [math.AP]

Guilherme Mazanti, Islam Boussaada, Silviu-Iulian Niculescu, Yacine Chitour. Effects of Roots of Maximal Multiplicity on the Stability of Some Classes of Delay Differential-Algebraic Systems: The Lossless Propagation Case. MTNS 2021 -24th International Symposium on Mathematical Theory of Networks and Systems, Aug 2021, Cambridge, United Kingdom. pp.764--769, ⟨10.1016/j.ifacol.2021.06.177⟩. ⟨hal-02463452v2⟩