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Pré-Publication, Document De Travail Année : 2023

Decay Rate Assignment through Multiple Spectral Values in Delay Systems

Résumé

This paper focuses on a spectral property for linear time-invariant (LTI) dynamical systems represented by delay-differential equations (DDEs) entitled multiplicity-induced-dominancy (MID), which consists, roughly speaking, in the spectral abscissa of the system being defined by a multiple spectral value. More precisely, we focus on the MID property for spectral values with over-order multiplicity, i.e., a multiplicity larger than the order of the DDE. We highlight the fact that a root of over-order multiplicity is necessarily a root of a particular polynomial, called the elimination-produced-polynomial, and we address the MID property using a suitable factorization of the corresponding characteristic function involving special functions of Kummer type. Additional results and discussion are provided in the case of the $n$-th order integrator, in particular on the local optimality of a multiple root. The derived results show how the delay can be further exploited as a control parameter and are applied to some problems of stabilization of standard benchmarks with prescribed exponential decay.
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Dates et versions

hal-04266228 , version 1 (31-10-2023)

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  • HAL Id : hal-04266228 , version 1

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Islam Boussaada, Guilherme Mazanti, Silviu-Iulian Niculescu, Wim Michiels. Decay Rate Assignment through Multiple Spectral Values in Delay Systems. 2023. ⟨hal-04266228⟩
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