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

Jie Chen (1) , P. Fu , Silviu-Iulian Niculescu (2) , Z. Guan

1 CSP - Center for Space Physics [Boston]
2 L2S - Laboratoire des signaux et systèmes

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.

Domaines: Automatique; Automatique / Robotique

Jie 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, 2010, 48 (8), pp.5583-5605. ⟨10.1137/080741719⟩. ⟨hal-00557801⟩