| Title:
|
An application of the second Lyapunov method to stability investigation of differential equations with deviations (English) |
| Author:
|
Khusainov, Denis |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
34 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
127-142 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper presents overview of applications of A. M. Lyapunov’s direct method to stability investigation of systems with argument delay. Methods of building Lyapunov-Krasovskiy funcionals for linear systems with constant coefficients are considered. Lyapunov quadratic forms are used to obtain applicable methods for stability investigation and estimation of solution convergence for linear stationary systems, as well as non-linear control systems and systems with quadratic and rational right hand sides. (English) |
| Keyword:
|
Stability |
| Keyword:
|
Lyapunov functional |
| Keyword:
|
asymptotic stability |
| MSC:
|
34D20 |
| MSC:
|
34K20 |
| MSC:
|
34K35 |
| MSC:
|
93D05 |
| idZBL:
|
Zbl 0915.34066 |
| idMR:
|
MR1629684 |
| . |
| Date available:
|
2009-02-17T10:10:45Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107639 |
| . |
| Reference:
|
[1] B. S. Razumikhin: Stability of Hereditary Systems.Science Publ., 1988 (Russian). MR 0984127 |
| Reference:
|
[2] N. N. Krasovskiy: Some Problems of Movement Stability Theory.Fizmatgiz Publ., Moscow 1959 (Russian). |
| Reference:
|
[3] V. B. Kolmanovsky V. R. Nosov: Stability and Periodic Regimes with Post-Effect.Science Publ., Moscow 1981 (Russian). |
| Reference:
|
[4] Jack K. Hale, Sjoerd M. Verduyn Lunel: Introduction to Functional Differential Equations.Springer-Verlag, New York-Heidelberg-Berlin 1993. MR 1243878 |
| Reference:
|
[5] Yu. M. Repin: On stability of solutions of equations with argument delay.Applied Mathematics and Mechanics, vol. 21 2, (1957), 253–261 (Russian). MR 0089961 |
| Reference:
|
[6] H. Wenzhang: Generalization of Lyapunov’s method in a linear system.J. Math. Anal. and Appl., vol. 142 1, (1989), 83–94. |
| Reference:
|
[7] D. Ya. Khusainov V. P. Marzeniuk: Optimizational method for linear systems with delay investigation.Cybernetics and System Analysis, 4, (1996), 88–93 (Russian). |
| Reference:
|
[8] D. Ya. Khusainov: On one method of building Lyapunov-Krasovskiy functionals for linear systems with delay argument.Ukrainian Mathematical Journal, vol. 41 3, (1989), 382–387 (Russian). MR 1001547 |
| Reference:
|
[9] D. Ya. Khusainov E. A. Yunkova: Estimation of delay value in linear differential systems with delay argument.Ukrainian Mathematical Journal, vol. 35 2, (1983), 261–264 (Russian). MR 0698071 |
| Reference:
|
[10] D. Ya. Khusainov: On exponential stability of linear systems with delay.Differential Equations, vol. 25 2, (1989), 357–359 (Russian). Zbl 0696.34054, MR 0994729 |
| Reference:
|
[11] D. Ya. Khusainov E. A. Yunkova: On closeness of solutions of linear systems with delay and corresponding systems without delay.Ukrainian Mathematical Journal, vol. 41 11, (1989), 1549–1552 (Russian). MR 1036499 |
| Reference:
|
[12] D. Ya. Khusainov A. G. Zhuykova: Stability Estimations for Non-Linear Control Systems with Delay Argument.Institute of Mathematics, Academy of Science of Ukraine, (preliminary edition) 1988 (Russian). |
| Reference:
|
[13] D. Ya. Khusainov A. V. Shatyrko: Lyapunov Function Method for Investigation of Differential-Functional System Stability.Kiev University Press, Kiev 1997 (Russian). MR 1486825 |
| Reference:
|
[14] D. Ya. Khusainov V. F. Davidov: Solution estimates of quadratic systems with delay.Functional Differential Equations, Israel Seminar, vol. 3 3–4, (1996), 345–356. MR 1459316 |
| Reference:
|
[15] D. Ya. Khusainov E. E. Shevelenko: Investigation of differential systems with rational right-hand side.Ukrainian Mathematical Journal, vol. 47 1, (1995), 1292–1299 (Russian). MR 1368138 |
| Reference:
|
[16] D. Ya. Khusainov E. E. Shevelenko: Investigation of rational systems with delay.Differential Equations, vol. 31 1, (1995), 175–177 (Russian). MR 1369871 |
| . |
