### Abstract

This paper concerns the input/output stability of two systems in closed-loop where stability is ensured by using open-loop properties of each subsystem. The literature is divided into consideration of time-domain and frequency-domain conditions. A complete time-domain approach is given by dissipative and topological separation theory, where both conditions are given in the time-domain. On the other hand, the frequency-domain integral quadratic constraints (IQCs) framework uses only frequency-domain conditions. Between both extremes, the classical multiplier approach and the time-domain IQC framework can be seen as hybrid versions where one condition is tested in the time-domain and other condition is tested in the frequency-domain. The time-domain is more natural for nonlinear systems, and subsystems may be unbounded in time-domain analysis. However, the frequency-domain has two advantages: firstly if one block is linear, then frequency-domain analysis leads to elegant graphical and/or LMI conditions; secondly noncausal multipliers can be used. Recently the connection between frequency domain IQCs and dissipativity has been studied. Here we use graph separation results to provide a unifying framework. In particular we show how a recent factorization result establishes a straightforward link, completing an analysis suggested previously. This factorization leads to a simple and insightful dissipative condition to analyse stability of the feedback interconnection.

Original language | English (US) |
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Title of host publication | 54rd IEEE Conference on Decision and Control,CDC 2015 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 5701-5706 |

Number of pages | 6 |

ISBN (Electronic) | 9781479978861 |

DOIs | |

State | Published - Feb 8 2015 |

Event | 54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan Duration: Dec 15 2015 → Dec 18 2015 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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Volume | 54rd IEEE Conference on Decision and Control,CDC 2015 |

ISSN (Print) | 0743-1546 |

### Other

Other | 54th IEEE Conference on Decision and Control, CDC 2015 |
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Country | Japan |

City | Osaka |

Period | 12/15/15 → 12/18/15 |

### Keywords

- Frequency-domain analysis
- Linear systems
- Nonlinear systems
- Stability analysis
- Standards
- Time-domain analysis
- Transfer functions

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## Cite this

*54rd IEEE Conference on Decision and Control,CDC 2015*(pp. 5701-5706). [7403114] (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2015.7403114