| Title:
|
Stability and sliding modes for a class of nonlinear time delay systems (English) |
| Author:
|
Răsvan, Vladimir |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
136 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
155-164 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The following time delay system $$ \dot {x} = Ax(t) + \sum _1^rbq_i^*x(t-\tau _i)-b\varphi (c^*x(t)) $$ is considered, where $\varphi \colon \mathbb {R}\to \mathbb {R}$ may have discontinuities, in particular at the origin. The solution is defined using the “redefined nonlinearity” concept. For such systems sliding modes are discussed and a frequency domain inequality for global asymptotic stability is given. (English) |
| Keyword:
|
time lag |
| Keyword:
|
extended nonlinearity |
| Keyword:
|
absolute stability |
| MSC:
|
34A36 |
| MSC:
|
34D20 |
| MSC:
|
34K20 |
| MSC:
|
93C23 |
| MSC:
|
93D10 |
| idZBL:
|
Zbl 1224.34246 |
| idMR:
|
MR2856132 |
| DOI:
|
10.21136/MB.2011.141578 |
| . |
| Date available:
|
2011-06-07T11:28:44Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141578 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] Gelig, A. Kh., Leonov, G. A., Yakubovich, V. A.: Stability of Nonlinear Systems with Non-unique Equilibrium State.Nauka, Moskva, 1978 Russian; World Scientific, Singapore, 2004. English. |
| Reference:
|
[5] Halanay, A.: Differential Equations. Stability. Oscillations.Time Lags. Academic Press, New York (1966). Zbl 0144.08701, MR 0216103 |
| Reference:
|
[6] Halanay, A.: On the controllability of linear difference-differential systems.Math. Systems Theory Econom. 2 (1969), 329-336 (1969). Zbl 0185.23601, MR 0321566, 10.1007/978-3-642-46196-5_16 |
| Reference:
|
[7] Popov, V. M.: Hyperstability of Control Systems.Editura Academiei, Bucharest & Springer, Berlin (1973). Zbl 0276.93033, MR 0387749 |
| Reference:
|
[8] Răsvan, Vl.: Absolute Stability of Time Lag Control Systems.Romanian Editura Academiei, Bucharest, 1975 improved Russian version by Nauka, Moskva, 1983. MR 0453048 |
| Reference:
|
[9] Răsvan, Vl., Danciu, D., Popescu, D.: Nonlinear and time delay systems for flight control.Math. Repts. 11 (2009), 359-367. Zbl 1212.34247, MR 2656171 |
| Reference:
|
[10] Richard, J. P., Gouaisbaut, F., Perruquetti, W.: Sliding mode control in the presence of delay.Kybernetika 37 (2001), 277-294. Zbl 1265.93046, MR 1859086 |
| . |
