### Abstract

Original language | English |
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Place of Publication | Tilburg |

Publisher | Finance |

Number of pages | 34 |

Volume | 2000-31 |

Publication status | Published - 2000 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 2000-31 |

### Fingerprint

### Keywords

- Optimal model reduction
- State space balancing
- l2-systems
- Least squares optimization
- Gap metrics
- Hankelnorm reduction

### Cite this

*Optimal Angle Reduction - A Behavioral Approach to Linear System Approximation*. (CentER Discussion Paper; Vol. 2000-31). Tilburg: Finance.

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**Optimal Angle Reduction - A Behavioral Approach to Linear System Approximation.** / Roorda, B.; Weiland, S.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Optimal Angle Reduction - A Behavioral Approach to Linear System Approximation

AU - Roorda, B.

AU - Weiland, S.

N1 - Pagination: 34

PY - 2000

Y1 - 2000

N2 - We investigate the problem of optimal state reduction under minimization of the angle between system behaviors. The angle is defined in a worst-case sense, as the largest angle that can occur between a system trajectory and its optimal approximation in the reduced order model. This problem is analysed for linear time-invariant finite dimensional systems, in a behavioral l2-setting, without reference to input/output decompositions and stability considerations. The notion of a weakest past-future link is introduced and it is shown how this concept is applied for the purpose of model reduction. A method that reduces the state dimension by one is presented and shown to be optimal. Specific algorithms are provided for the numerical implementation of the approximation method.

AB - We investigate the problem of optimal state reduction under minimization of the angle between system behaviors. The angle is defined in a worst-case sense, as the largest angle that can occur between a system trajectory and its optimal approximation in the reduced order model. This problem is analysed for linear time-invariant finite dimensional systems, in a behavioral l2-setting, without reference to input/output decompositions and stability considerations. The notion of a weakest past-future link is introduced and it is shown how this concept is applied for the purpose of model reduction. A method that reduces the state dimension by one is presented and shown to be optimal. Specific algorithms are provided for the numerical implementation of the approximation method.

KW - Optimal model reduction

KW - State space balancing

KW - l2-systems

KW - Least squares optimization

KW - Gap metrics

KW - Hankelnorm reduction

M3 - Discussion paper

VL - 2000-31

T3 - CentER Discussion Paper

BT - Optimal Angle Reduction - A Behavioral Approach to Linear System Approximation

PB - Finance

CY - Tilburg

ER -