An Eigenvalue Perturbation Approach to Stability Analysis, Part II: When Will Zeros of Time-Delay Systems Cross Imaginary Axis?

Authors:
Jie Chen;Peilin Fu;Silviu-Iulian Niculescu;Zhihong Guan
Affiliations:
jchen@ee.ucr.edu;pfu@nu.edu;Silviu.Niculescu@lss.supelec.fr;zhguan@mail.hust.edu.cn
Venue:
SIAM Journal on Control and Optimization
Year:
2010

Citing 6
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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.