| Title:
|
Preservation of exponential stability for equations with several delays (English) |
| Author:
|
Berezansky, Leonid |
| Author:
|
Braverman, Elena |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
136 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
135-144 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider preservation of exponential stability for the scalar nonoscillatory linear equation with several delays $$ \dot {x}(t) + \sum _{k=1}^m a_k(t) x(h_k(t)) = 0, \quad a_k(t) \geq 0 $$ under the addition of new terms and a delay perturbation. We assume that the original equation has a positive fundamental function; our method is based on Bohl-Perron type theorems. Explicit stability conditions are obtained. (English) |
| Keyword:
|
exponential stability |
| Keyword:
|
nonoscillation |
| Keyword:
|
explicit stability condition |
| Keyword:
|
perturbation |
| MSC:
|
34K06 |
| MSC:
|
34K20 |
| MSC:
|
34K27 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1224.34240 |
| idMR:
|
MR2856129 |
| DOI:
|
10.21136/MB.2011.141576 |
| . |
| Date available:
|
2011-06-07T11:27:28Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141576 |
| . |
| Reference:
|
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| Reference:
|
[2] Berezansky, L., Braverman, E.: Preservation of the exponential stability under perturbations of linear delay impulsive differential equations.Z. Anal. Anwendungen 14 (1995), 157-174. Zbl 0821.34072, MR 1327497, 10.4171/ZAA/668 |
| Reference:
|
[3] Hale, J. K., Lunel, S. M. Verduyn: Introduction to Functional Differential Equations.Applied Mathematical Sciences, Vol. 99, Springer, New York (1993). MR 1243878, 10.1007/978-1-4612-4342-7_3 |
| Reference:
|
[4] Azbelev, N. V., Berezansky, L., Rakhmatullina, L. F.: A linear functional-differential equation of evolution type.Differ. Equations 13 (1977), 1331-1339. |
| Reference:
|
[5] Azbelev, N. V., Berezansky, L., Simonov, P. M., Chistyakov, A. V.: The stability of linear systems with aftereffect I.Differ. Equations 23 (1987), 493-500;
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| Reference:
|
[6] Azbelev, N. V., Simonov, P. M.: Stability of Differential Equations with Aftereffect.Stability and Control: Theory, Methods and Applications, Vol. 20. Taylor & Francis, London (2003). Zbl 1049.34090, MR 1965019 |
| Reference:
|
[7] Berezansky, L., Braverman, E.: Nonoscillation and exponential stability of delay differential equations with oscillating coefficients.J. Dyn. Control Syst. 15 (2009), 63-82. Zbl 1203.34103, MR 2475661, 10.1007/s10883-008-9058-4 |
| Reference:
|
[8] Györi, I., Ladas, G.: Oscillation Theory of Delay Differential Equations with Applications.Clarendon Press, Oxford University Press, New York (1991). MR 1168471 |
| . |
