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 |

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Category: | math |

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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 |

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Date available: | 2010-06-02T18:37:45Z |

Last updated: | 2012-06-06 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/140010 |

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