On Qualitative Properties of Low-Degree Quasipolynomials: Further remarks on the spectral abscissa and rightmost-roots assignment

Souad Amrane; Fazia Bedouhene; Islam Boussaada; Silviu-Iulian Niculescu

On Qualitative Properties of Low-Degree Quasipolynomials: Further remarks on the spectral abscissa and rightmost-roots assignment

Souad Amrane ^{1, 2} Fazia Bedouhene ² Islam Boussaada ^{3, 4} Silviu-Iulian Niculescu ⁵

1 University of Tizi-Ouzou

2 LMPA - Laboratoire de Mathématiques Pures et Appliquées [Tizi-Ouzou]

3 L2S - Laboratoire des signaux et systèmes

4 DISCO - Dynamical Interconnected Systems in COmplex Environments

L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506

5 Division Systèmes - L2S

L2S - Laboratoire des signaux et systèmes : 1289

Abstract : The present study concerns a frequency domain approach in the stability analysis and stabilization via reduced-order controller design for linear time-invariant retarded Time-delay systems. More precisely, we address the problem of the spectral abscissa characterization and the coexistence of non oscillating modes for such functional differential equations. The design approach we propose is merely a delayed-output-feedback where the candidates' parameters result from the manifold defined by the coexistence of an exact number of negative spectral values, which guarantees the asymptotic stability of the system's solutions. The dominancy of such non oscillating modes is analytically shown for the considered reduced order Time-delay systems. Finally, using the W-Lambert function, further description of the spectrum distribution is presented.

Keywords : Time-delay systems Stability Spectral abscissa Control design Pole assignment

Document type :

Journal articles

Domain :

Engineering Sciences [physics] / Automatic

Mathematics [math] / Dynamical Systems [math.DS]

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https://hal-centralesupelec.archives-ouvertes.fr/hal-01969066
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Submitted on : Thursday, January 3, 2019 - 4:10:04 PM
Last modification on : Tuesday, June 4, 2019 - 11:08:06 AM
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