Decay Rate Assignment through Multiple Spectral Values in Delay Systems - Archive ouverte HAL
Article Dans Une Revue IEEE Transactions on Automatic Control Année : 2024

Decay Rate Assignment through Multiple Spectral Values in Delay Systems

Résumé

This article focuses on a spectral property for linear time-invariant 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 overorder multiplicity, i.e., a multiplicity larger than the order of the DDE. We highlight the fact that a root of overorder 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)
hal-04266228 , version 2 (27-09-2024)

Identifiants

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Islam Boussaada, Guilherme Mazanti, Silviu-Iulian Niculescu, Wim Michiels. Decay Rate Assignment through Multiple Spectral Values in Delay Systems. IEEE Transactions on Automatic Control, inPress, ⟨10.1109/TAC.2024.3447117⟩. ⟨hal-04266228v2⟩
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