On computing Puiseux series for multiple imaginary characteristic roots of LTI delay systems with commensurate delays

Xu-Guang Li 1 Silviu-Iulian Niculescu 2 Arben Cela 3 Hong-Hai Wang 1 Tiao-Yang Cai 1
2 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
Abstract : Obtaining the Puiseux series of multiple imaginary (characteristic) roots (MIRs) is a fundamental issue in the stability analysis of time-delay systems. However, to the best of the authors' knowledge, this issue has not been fully investigated up to date. This note focuses on the Puiseux series expansion of MIRs of linear time-invariant systems including commensurate delays. For an MIR of any multiplicity, we propose an algorithm for defining the structure of the Puiseux series, as well as the explicit computation of the corresponding coefficients. By using the proposed method, we can find all the Puiseux series corresponding to all the root loci.
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Submitted on : Thursday, January 23, 2014 - 3:04:21 PM
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Xu-Guang Li, Silviu-Iulian Niculescu, Arben Cela, Hong-Hai Wang, Tiao-Yang Cai. On computing Puiseux series for multiple imaginary characteristic roots of LTI delay systems with commensurate delays. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2013, 58 (5), pp.1338-1343. ⟨10.1109/TAC.2012.2226102⟩. ⟨hal-00935428⟩

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