An eigenvalue perturbation approach to stability analysis, Part 2 : When will zeros of time-delay systems cross imaginary axis ?

Abstract : This paper presents an application of the eigenvalue series developed in Part I [J. Chen et al., SIAM J. Control Optim., 48 (2010), pp. 5564-5582] to the study of linear time-invariant delay systems, focusing on the asymptotic behavior of critical characteristic zeros on the imaginary axis. We consider systems given in state-space form and as quasi-polynomials, and we develop an eigenvalue perturbation analysis approach which appears to be both conceptually appealing and computationally efficient. Our results reveal that the zero asymptotic behavior of time-delay systems can in general be characterized by solving a simple eigenvalue problem, and, additionally, when described by a quasi-polynomial, by computing the derivatives of the quasipolynomial.
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Submitted on : Thursday, January 20, 2011 - 9:44:28 AM
Last modification on : Wednesday, September 18, 2019 - 12:08:32 PM

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J. Chen, P. Fu, Silviu-Iulian Niculescu, Z. Guan. An eigenvalue perturbation approach to stability analysis, Part 2 : When will zeros of time-delay systems cross imaginary axis ?. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2010, 48 (8), pp.5583-5605. ⟨10.1137/080741719⟩. ⟨hal-00557801⟩

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