| Title:
|
Determining the domain of attraction of hybrid non–linear systems using maximal Lyapunov functions (English) |
| Author:
|
Rozgonyi, Szabolcs |
| Author:
|
Hangos, Katalin M. |
| Author:
|
Szederkényi, Gábor |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
19-37 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this article a method is presented to find systematically the domain of attraction (DOA) of hybrid non-linear systems. It has already been shown that there exists a sequence of special kind of Lyapunov functions $V_n$ in a rational functional form approximating a maximal Lyapunov function $V_M$ that can be used to find an estimation for the DOA. Based on this idea, an improved method has been developed and implemented in a Mathematica-package to find such Lyapunov functions $V_n$ for a class of hybrid (piecewise non-linear) systems, where the dynamics is continuous on the boundary of the different regimes in the state space. In addition, a computationally feasible method is proposed to estimate the DOA using a maximal fitting hypersphere. (English) |
| Keyword:
|
maximal Lyapunov functions |
| Keyword:
|
domain of attraction |
| Keyword:
|
hybrid systems |
| MSC:
|
34A34 |
| MSC:
|
34A38 |
| MSC:
|
34D20 |
| MSC:
|
34D23 |
| MSC:
|
34D35 |
| MSC:
|
37B25 |
| MSC:
|
70K20 |
| MSC:
|
93D20 |
| idZBL:
|
Zbl 1194.34018 |
| idMR:
|
MR2666892 |
| . |
| Date available:
|
2010-06-02T19:39:30Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140048 |
| . |
| Reference:
|
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