### 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 |
---|---|

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 |

### Fingerprint

### 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

### 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

**Finite-dimensional characterizations of H ^{∞} control for linear systems with delays in input and output.** / Uchida, Kenko; Ikeda, K.; Azuma, T.; Kojima, A.

Research output: Contribution to journal › Article

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

*International Journal of Robust and Nonlinear Control*, vol. 13, no. 9, pp. 833-843. https://doi.org/10.1002/rnc.848

^{∞}control for linear systems with delays in input and output. International Journal of Robust and Nonlinear Control. 2003 Jul 30;13(9):833-843. https://doi.org/10.1002/rnc.848

}

TY - JOUR

T1 - Finite-dimensional characterizations of H∞ control for linear systems with delays in input and output

AU - Uchida, Kenko

AU - Ikeda, K.

AU - Azuma, T.

AU - Kojima, A.

PY - 2003/7/30

Y1 - 2003/7/30

N2 - 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.

AB - 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.

KW - Finite-dimensional characterization

KW - H control

KW - Input delay

KW - Linear time-delay system

KW - Output delay

KW - Prediction condition

UR - http://www.scopus.com/inward/record.url?scp=0041306904&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041306904&partnerID=8YFLogxK

U2 - 10.1002/rnc.848

DO - 10.1002/rnc.848

M3 - Article

VL - 13

SP - 833

EP - 843

JO - International Journal of Robust and Nonlinear Control

JF - International Journal of Robust and Nonlinear Control

SN - 1049-8923

IS - 9

ER -