### Abstract

We formulate H^{∞} control problems for linear systems with delays in input and output, and discuss possibility of finite-dimensional characterizations of solutions. In the case when delay exists in control input and controlled output, first, we derive an output feedback H^{∞} control formula of the central solution type, which is given by using solutions of finite- and infinite-dimensional Riccati matrix inequalities. Second, we show that, if the controlled output is chosen such that it satisfies the 'prediction condition', the solution to the infinite-dimensional Riccati inequality can be calculated by solving a finite-dimensional Riccati inequality. We provide a system theoretic interpretation for the prediction condition, and show that, if the prediction condition is satisfied, there is an equivalent H^{∞} control problem for finite-dimensional linear systems with no delay. Finally, the equivalence result is extended to the case when delay exists also in measurement output.

Original language | English |
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Pages (from-to) | 833-843 |

Number of pages | 11 |

Journal | International Journal of Robust and Nonlinear Control |

Volume | 13 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2003 Jul 30 |

### Keywords

- Finite-dimensional characterization
- H control
- Input delay
- Linear time-delay system
- Output delay
- Prediction condition

### ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering
- Applied Mathematics

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## Cite this

^{∞}control for linear systems with delays in input and output.

*International Journal of Robust and Nonlinear Control*,

*13*(9), 833-843. https://doi.org/10.1002/rnc.848