Insights on asymptotic behavior of characteristic roots of quasi-polynomials with delay-dependent coefficients in some ill-posed cases

A. Martínez-González , César Fernando Méndez Barrios (1) , Silviu-Iulian Niculescu (2) , Jie Chen (3)

1 UASLP - Universidad Autonoma de San Luis Potosi [México]
2 L2S - Laboratoire des signaux et systèmes
3 CUHK - City University of Hong Kong [Hong Kong]

This work focus on the asymptotic behavior of critical roots of linear time-delay systems with delay-dependent coefficients. Our main goal is to derive a simple methodology to characterize some ill-posed cases from the open literature. In order to accomplish such a task, our main tool will be to express the solutions as a convergent power series. More specifically, by means of an appropriate change of variable, the expansion of unbounded solutions is obtained, which allows to derive an appropriate auxiliary solution that serves to analyze the behavior of such solutions. One of the main benefits in adopting such an approach, is that stability analysis in the ill-posed cases can also be covered.

Domains: Automatic Control Engineering

A. Martínez-González, César Fernando Méndez Barrios, Silviu-Iulian Niculescu, Jie Chen. Insights on asymptotic behavior of characteristic roots of quasi-polynomials with delay-dependent coefficients in some ill-posed cases. 7th Symposium on System Structure and Control (SSSC) and 15th workshop on time-delay systems (TDS), Islam Boussaada; Y Bouzidi; A Quadrat, Sep 2019, Sinaia, Romania. ⟨10.1016/j.ifacol.2019.12.209⟩. ⟨hal-02329207⟩