Invariance properties for a class of quasipolynomials

Xu-Guang Li 1 Silviu-Iulian Niculescu 2, 3, 4 Arben Cela 5 Hong-Hai Wang 1 Tiao-Yang Cai 1
3 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
4 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
Abstract : When a time-delay system involves multiple imaginary roots (MIRs), the stability analysis will become much more complicated than that in the case with only simple imaginary roots (SIRs). An MIR may exhibit different splitting behaviors and, to the best of the authors' knowledge, their properties have not been fully investigated. In this paper, we focus on characterizing the invariance properties for MIRs with any multiplicity. Furthermore, the proposed methodology makes it possible to also cover some degenerate cases already encountered and discussed in the literature. In addition, we propose an easily implemented frequency-sweeping method, making it possible to derive the asymptotic behavior without invoking the Puiseux series.
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Xu-Guang Li, Silviu-Iulian Niculescu, Arben Cela, Hong-Hai Wang, Tiao-Yang Cai. Invariance properties for a class of quasipolynomials. Automatica, Elsevier, 2014, 50 (3), pp.890-895. ⟨10.1016/j.automatica.2013.12.007⟩. ⟨hal-00935376⟩



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