| Title:
|
The existence of limit cycle for perturbed bilinear systems (English) |
| Author:
|
Damak, Hanen |
| Author:
|
Hammami, Mohamed Ali |
| Author:
|
Sun, Yeong-Jeu |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
48 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
177-189 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, the feedback control for a class of bilinear control systems with a small parameter is proposed to guarantee the existence of limit cycle. We use the perturbation method of seeking in approximate solution as a finite Taylor expansion of the exact solution. This perturbation method is to exploit the “smallness” of the perturbation parameter $\varepsilon$ to construct an approximate periodic solution. Furthermore, some simulation results are given to illustrate the existence of a limit cycle for this class of nonlinear control systems. (English) |
| Keyword:
|
perturbed bilinear system |
| Keyword:
|
feedback control |
| Keyword:
|
limit cycle |
| MSC:
|
37G15 |
| MSC:
|
70K05 |
| idMR:
|
MR2954318 |
| . |
| Date available:
|
2012-05-15T16:06:28Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142806 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] H. K. Khalil: Nonlinear Systems..Prentice-Hall, New York 2002. Zbl 1194.93083 |
| Reference:
|
[4] A. I. Mees: Limit cycles stability..IMA J. Appl. Math. 11 (1972), 3, 281-295. MR 0366468 |
| Reference:
|
[5] R. Miller, A. Michel, G. S. Krenz: On the stability of limit cycles in nonlinear feedback systems: analysis using describing functions..IEEE Trans. Circuits and Systems 30 (1983), 9, 684-696. Zbl 0536.93041, MR 0718403, 10.1109/TCS.1983.1085408 |
| Reference:
|
[6] Y. Sun: Limit cycles design for a class of bilinear control systems..Chaos, Solitons and Fractals 33 (2007), 156-162. Zbl 1152.93395, MR 2301853, 10.1016/j.chaos.2006.01.004 |
| Reference:
|
[7] Y. Sun: Existence and uniqueness of limit cycle for a class of nonlinear discrete-time systems..Chaos, Solitons and Fractals 38 (2008), 89-96. Zbl 1142.39307, MR 2417646, 10.1016/j.chaos.2006.10.031 |
| Reference:
|
[8] Y. Sun: The existence of the exponentially stable limit cycle for a class of nonlinear systems..Chaos, Solitons and Fractals 39 (2009), 2357-2362. Zbl 1197.34045, 10.1016/j.chaos.2007.07.006 |
| . |
