Multiplicity-Induced-Dominancy property for second-order neutral differential equations with application in oscillation damping

Amina Benarab (1, 2, 3) , Islam Boussaada (1, 2, 3) , Karim Trabelsi (1) , Catherine Bonnet (2, 3)

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

This paper addresses the exponential stability of linear time-delay systems of neutral type. In general, it is quite a challenge to establish conditions on the parameters of the system in order to guarantee such a stability. Recent works emphasized the link between maximal multiplicity and dominant roots. Indeed, conditions for a given multiple root to be necessarily dominant are investigated, this property is known as Multiplicity-Induced-Dominancy (MID). The aim of this paper is to explore the effect of multiple roots with admissible multiplicities exhibiting, under appropriate conditions, the validity of the MID property for second-order neutral time-delay differential equations with a single delay. The ensuing control methodology is summarized in a five-steps algorithm that can be exploited in the design of higher-order systems. The main ingredient of the proposed method is the dominancy proof for multiple spectral values based on frequency bounds established via integral equations. As an illustration, the stabilization of the classical oscillator benefits from the obtained results.

Mots clés: Delay Systems; Neutral Functional Differential Equations; Classical Oscillator; Multiplicity-Induced-Dominancy

Domaines: Automatique / Robotique; Systèmes et contrôle [cs.SY]; Equations aux dérivées partielles [math.AP]; Science non linéaire [physics]

Amina Benarab, Islam Boussaada, Karim Trabelsi, Catherine Bonnet. Multiplicity-Induced-Dominancy property for second-order neutral differential equations with application in oscillation damping. European Journal of Control, 2023, 69, ⟨10.1016/j.ejcon.2022.100721⟩. ⟨hal-03626756⟩