### Abstract

The paper provides a formulation of the quadratic separator result in a fairly general input-output operator framework and it focuses on the specific points that are different compared to the usual finite dimensional formulations. The major contribution of the paper is to emphasize the role of the causality in obtaining the stability result having a quadratic separator and the fact that the plant and the boundedness constant in the formulation of the well-posedness condition determine the robust stability domain associated to the given plant, i.e., the set of those systems {κ} that stabilizes the given plant and produce the given "disturbance rejection" level γ. Concerning the causality issue the necessity of the homotopy argument in the IQC results is also explained and its relation with a general result concerning nest algebras is pointed out.

Original language | English |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1756-1761 |

Number of pages | 6 |

ISBN (Print) | 9781467357173 |

DOIs | |

Publication status | Published - 2013 |

Event | 52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy Duration: Dec 10 2013 → Dec 13 2013 |

### Other

Other | 52nd IEEE Conference on Decision and Control, CDC 2013 |
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Country | Italy |

City | Florence |

Period | 12/10/13 → 12/13/13 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*(pp. 1756-1761). [6760136] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6760136

**Quadratic separators in the input-output setting.** / Szabó, Z.; Biró, Zs; Bokor, J.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the IEEE Conference on Decision and Control.*, 6760136, Institute of Electrical and Electronics Engineers Inc., pp. 1756-1761, 52nd IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, 12/10/13. https://doi.org/10.1109/CDC.2013.6760136

}

TY - GEN

T1 - Quadratic separators in the input-output setting

AU - Szabó, Z.

AU - Biró, Zs

AU - Bokor, J.

PY - 2013

Y1 - 2013

N2 - The paper provides a formulation of the quadratic separator result in a fairly general input-output operator framework and it focuses on the specific points that are different compared to the usual finite dimensional formulations. The major contribution of the paper is to emphasize the role of the causality in obtaining the stability result having a quadratic separator and the fact that the plant and the boundedness constant in the formulation of the well-posedness condition determine the robust stability domain associated to the given plant, i.e., the set of those systems {κ} that stabilizes the given plant and produce the given "disturbance rejection" level γ. Concerning the causality issue the necessity of the homotopy argument in the IQC results is also explained and its relation with a general result concerning nest algebras is pointed out.

AB - The paper provides a formulation of the quadratic separator result in a fairly general input-output operator framework and it focuses on the specific points that are different compared to the usual finite dimensional formulations. The major contribution of the paper is to emphasize the role of the causality in obtaining the stability result having a quadratic separator and the fact that the plant and the boundedness constant in the formulation of the well-posedness condition determine the robust stability domain associated to the given plant, i.e., the set of those systems {κ} that stabilizes the given plant and produce the given "disturbance rejection" level γ. Concerning the causality issue the necessity of the homotopy argument in the IQC results is also explained and its relation with a general result concerning nest algebras is pointed out.

UR - http://www.scopus.com/inward/record.url?scp=84902309960&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902309960&partnerID=8YFLogxK

U2 - 10.1109/CDC.2013.6760136

DO - 10.1109/CDC.2013.6760136

M3 - Conference contribution

AN - SCOPUS:84902309960

SN - 9781467357173

SP - 1756

EP - 1761

BT - Proceedings of the IEEE Conference on Decision and Control

PB - Institute of Electrical and Electronics Engineers Inc.

ER -