Title: | Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems (English) |

Author: | Ikeda, Kojiro |

Author: | Azuma, Takehito |

Author: | Uchida, Kenko |

Language: | English |

Journal: | Kybernetika |

ISSN: | 0023-5954 |

Volume: | 37 |

Issue: | 4 |

Year: | 2001 |

Pages: | [505]-520 |

Summary lang: | English |

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Category: | math |

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Summary: | This paper considers an analysis and synthesis problem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops an Linear Matrix Inequality (LMI) approach. First, we present an existence condition and an explicit formula of controllers, which guarantee a prescribed level of $L^2$ gain of closed loop systems, in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for the cases of delay- independent/dependent and memoryless/memory controllers, while the infinity dimensionality of the LMIs makes the result difficult to apply. Second, we introduce a technique to reduce the infinite-dimensional LMIs to a finite number of LMIs, and present a feasible algorithm for synthesis of controllers based on the finite-dimensional LMIs. (English) |

Keyword: | time-delay system |

Keyword: | linear system |

Keyword: | LMI |

MSC: | 93B50 |

MSC: | 93B51 |

MSC: | 93C23 |

MSC: | 93D05 |

idZBL: | Zbl 1265.93146 |

idMR: | MR1859098 |

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Date available: | 2009-09-24T19:41:20Z |

Last updated: | 2015-03-26 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/135423 |

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Reference: | [1] Azuma T., Ikeda, K., Uchida K.: Infinite-dimensional LMI approach to $H^\infty $ control synthesis for linear systems with time-delay.In: Proc. of ECC99, 1999 |

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Reference: | [12] Ikeda K., Azuma, T., Uchida K.: A construction method of convex polyhedron in infinite number LMI approach for linear time-delay systems.In: Proc. of Annual Meeting of IEEJ 2000, pp. 1006–1007 (in Japanese) |

Reference: | [13] Ikeda K., Uchida K.: Analysis of state reachable sets for linear time-delay systems.In: Proc. of SICE2000, #105A-1 (in Japanese) |

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