### Abstract

We consider the pole assignment problems for time-invariant linear and quadratic control systems, with time-delay in the control. Closed-loop eigenvectors in X=[x_{1},x_{2},...] are chosen from their corresponding invariant subspaces, possibly optimizing some robustness measure, and explicit expressions for the feedback matrices are given in terms of X. Condition of the problems is also investigated. Our approach extends the well-known Kautsky, Nichols, and VanDooren algorithm. Consequently, the results are similar to those for systems without time-delay, except for the presence of the 'secondary' eigenvalues and the condition of the problems. Simple illustrative numerical examples are given.

Original language | English |
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Pages (from-to) | 291-301 |

Number of pages | 11 |

Journal | Numerical Linear Algebra with Applications |

Volume | 20 |

Issue number | 2 |

DOIs | |

Publication status | Published - Mar 2013 |

Externally published | Yes |

### Keywords

- Linear system
- Pole assignment
- Quadratic system
- Robustness
- Time-delay