### Abstract

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.

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 |

### Keywords

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

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## Cite this

Roorda, B., & Weiland, S. (2000).

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