Necessary and sufficient condition for neutral-type delay systems: Polynomial approximations
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918244937367552 |
|---|---|
| author | Portilla, Gerson Bajodek, Mathieu Mondié, Sabine |
| author_facet | Portilla, Gerson Bajodek, Mathieu Mondié, Sabine |
| contents | A new necessary and sufficient stability test in a tractable number of operations for linear neutral-type delay systems is introduced. It is developed in the Lyapunov-Krasovskii framework via functionals with prescribed derivatives. The necessary conditions, which stem from substituting any polynomial approximation of the functional argument, reduce to a quadratic form of monomials whose matrix is independent of the coefficients of the approximation under consideration. In the particular case of Chebyshev polynomials, the functional approximation error is quantified, leading to an estimate of the order of approximation such that the positive semi-definiteness of the functional is verified. Some examples illustrate the obtained results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Necessary and sufficient condition for neutral-type delay systems: Polynomial approximations Portilla, Gerson Bajodek, Mathieu Mondié, Sabine Systems and Control A new necessary and sufficient stability test in a tractable number of operations for linear neutral-type delay systems is introduced. It is developed in the Lyapunov-Krasovskii framework via functionals with prescribed derivatives. The necessary conditions, which stem from substituting any polynomial approximation of the functional argument, reduce to a quadratic form of monomials whose matrix is independent of the coefficients of the approximation under consideration. In the particular case of Chebyshev polynomials, the functional approximation error is quantified, leading to an estimate of the order of approximation such that the positive semi-definiteness of the functional is verified. Some examples illustrate the obtained results. |
| title | Necessary and sufficient condition for neutral-type delay systems: Polynomial approximations |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2406.15581 |