### Abstract

This paper considers a synthesis problem of H<sup>∞</sup> controllers for linear systems with time delay in the form of delay-dependent memory state feedback, and develops a new Linear Matrix Inequalities (LMIs) approach. First, we present an existence condition and an explicit formula of H<sup>∞</sup> controllers 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 H<sup>∞</sup> controllers based on the finite-dimensional LMIs.

Original language | English |
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Title of host publication | European Control Conference, ECC 1999 - Conference Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 3655-3660 |

Number of pages | 6 |

ISBN (Print) | 9783952417355 |

Publication status | Published - 2015 Mar 24 |

Event | 1999 European Control Conference, ECC 1999 - Karlsruhe, Germany Duration: 1999 Aug 31 → 1999 Sep 3 |

### Other

Other | 1999 European Control Conference, ECC 1999 |
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Country | Germany |

City | Karlsruhe |

Period | 99/8/31 → 99/9/3 |

### Keywords

- H<sup>∞</sup> control synthesis problem
- Linear Matrix Inequalities
- Memory state feedback controllers
- Time delay systems

### ASJC Scopus subject areas

- Control and Systems Engineering

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## Cite this

*European Control Conference, ECC 1999 - Conference Proceedings*(pp. 3655-3660). [7099898] Institute of Electrical and Electronics Engineers Inc..