| Title:
|
Geometric structures of stable output feedback systems (English) |
| Author:
|
Zhang, Zhenning |
| Author:
|
Sun, Huafei |
| Author:
|
Zhong, Fengwei |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
387-404 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we investigate the geometric structures of the stable time-varying and the stable static output feedback systems. Firstly, we give a parametrization of stabilizing time-varying output feedback gains subject to certain constraints, that is, the subset of stabilizing time-varying output feedback gains is diffeomorphic to the Cartesian product of the set of time-varying positive definite matrices and the set of time-varying skew symmetric matrices satisfying certain algebraic conditions. Further, we show how the Cartesian product satisfying certain algebraic conditions is imbedded into the Cartesian product of the set of time-varying positive definite matrices and the set of time-varying skew symmetric matrices. Then, we give some eigenvalue properties of the stable time-varying output feedback systems. Notice that the stable static output feedback system, which does not depend on the temporal parameter $t$, is just a special case of the stable time-varying output feedback system. Moreover, we use the Riemannian metric, the connections and the curvatures to describe the subset of stabilizing static output feedback gains. At last, we use a static output feedback system to illustrate our conclusions. (English) |
| Keyword:
|
diffeomorphism |
| Keyword:
|
geometric structure |
| Keyword:
|
output feedback |
| Keyword:
|
immersion |
| MSC:
|
53B20 |
| MSC:
|
58E25 |
| MSC:
|
93B27 |
| MSC:
|
93D15 |
| idZBL:
|
Zbl 1169.53316 |
| idMR:
|
MR2543129 |
| . |
| Date available:
|
2010-06-02T18:37:45Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140010 |
| . |
| Reference:
|
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| . |
