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Article Dans Une Revue Systems and Control Letters Année : 2024

Insights on equidistributed real spectral values in second-order delay systems: perspectives in partial pole placement

Résumé

In this work, we show that the coexistence of the maximal number of real spectral values of generic single-delay retarded second-order differential equations guarantees the realness of the rightmost spectral value. From a control theory standpoint, this entails that a delayed proportional-derivative (PD) controller can stabilize a delayed second-order differential equation. By assigning the maximum number of negative roots to the corresponding characteristic function (a quasipolynomial), we establish the conditions for asymptotic stability. If the assigned real spectral values are uniformly distributed, we specify a necessary and sufficient condition for the rightmost root to be negative, thus guaranteeing the exponential decay rate of the system’s solutions. We illustrate the proposed design methodology in the delayed PD control of the damped harmonic oscillator. It is worth mentioning that this work represents a natural continuation of Amrane et al. (2018) and Bedouhene et al. (2020), addressing the problem of coexisting real spectral values for linear dynamical systems including delays in their models.
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Dates et versions

hal-04145041 , version 1 (28-06-2023)
hal-04145041 , version 2 (22-01-2024)

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Paternité - Pas d'utilisation commerciale - Partage selon les Conditions Initiales

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Timothée Schmoderer, Islam Boussaada, Silviu-Iulian Niculescu, Fazia Bedouhene. Insights on equidistributed real spectral values in second-order delay systems: perspectives in partial pole placement. Systems and Control Letters, 2024, 185, pp.105728. ⟨10.1016/j.sysconle.2024.105728⟩. ⟨hal-04145041v2⟩
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