| Title:
|
Delay-dependent stability conditions for fundamental characteristic functions (English) |
| Author:
|
Matsunaga, Hideaki |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2023 |
| Pages:
|
77-84 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper is devoted to the investigation on the stability for two characteristic functions $f_1(z) = z^2+pe^{-z\tau }+q$ and $f_2(z) = z^2+pz e^{-z\tau }+q$, where $p$ and $q$ are real numbers and $\tau >0$. The obtained theorems describe the explicit stability dependence on the changing delay $\tau $. Our results are applied to some special cases of a linear differential system with delay in the diagonal terms and delay-dependent stability conditions are obtained. (English) |
| Keyword:
|
characteristic equation |
| Keyword:
|
delay |
| Keyword:
|
stability switch |
| MSC:
|
34K20 |
| MSC:
|
34K25 |
| idZBL:
|
Zbl 07675576 |
| idMR:
|
MR4563018 |
| DOI:
|
10.5817/AM2023-1-77 |
| . |
| Date available:
|
2023-02-22T14:28:24Z |
| Last updated:
|
2023-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151552 |
| . |
| Reference:
|
[1] Čermák, J., Kisela, T.: Stabilization and destabilization of fractional oscillators via a delayed feedback control.Commun. Nonlinear Sci. Numer. Simul. 117 (2023), 16 pp., Paper No. 106960. MR 4505440, 10.1016/j.cnsns.2022.106960 |
| Reference:
|
[2] Cooke, K.L., Grossman, Z.: Discrete delay, distributed delay and stability switches.J. Math. Anal. Appl. 86 (1982), 592–627. 10.1016/0022-247X(82)90243-8 |
| Reference:
|
[3] Freedman, H.I., Kuang, Y.: Stability switches in linear scalar neutral delay equations.Funkcial. Ekvac. 34 (1991), 187–209. |
| Reference:
|
[4] Hata, Y., Matsunaga, H.: Delay-dependent stability switches in a delay differential system.submitted for publication. |
| Reference:
|
[5] Hsu, C.S., Bhatt, S.J.: Stability charts for second-order dynamical systems with time lag.J. Appl. Mech. 33 (1966), 119–124. 10.1115/1.3624968 |
| Reference:
|
[6] Matsunaga, H.: Stability switches in a system of linear differential equations with diagonal delay.Appl. Math. Comput. 212 (2009), 145–152. MR 2519266, 10.1016/j.amc.2009.02.010 |
| Reference:
|
[7] Stépán, G.: Retarded Dynamical Systems: Stability and Characteristic Functions.Longman Scientific & Technical, New York, 1989. |
| . |
