### Abstract

We consider a linear control loop with time-varying delays, assumed to be independent and identically distributed random variables following a known probability distribution. We provide Nyquist criteria to assert the convergence to zero of the state statistical moments. The criterion pertaining to the first order moments parallels the one for deterministic time-invariant control loops. In particular, one can determine gain and phase margins. This criterion can be used to assert almost sure stability for positive linear systems. The criterion for the second order moments can be used to assert mean square stability for general linear systems. The applicability of the results is illustrated through a numerical example.

Language | English |
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Title of host publication | 2018 IEEE Conference on Decision and Control, CDC 2018 |

Place of Publication | Piscataway |

Publisher | Institute of Electrical and Electronics Engineers |

Pages | 270-275 |

Number of pages | 6 |

ISBN (Electronic) | 978-1-5386-1395-5 |

ISBN (Print) | 978-1-5386-1396-2 |

DOIs | |

State | Published - 18 Jan 2019 |

Event | 57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018 Conference number: 57 |

### Conference

Conference | 57th IEEE Conference on Decision and Control, CDC 2018 |
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Abbreviated title | CDC 2018 |

Country | United States |

City | Miami |

Period | 17/12/18 → 19/12/18 |

### Fingerprint

### Cite this

*2018 IEEE Conference on Decision and Control, CDC 2018*(pp. 270-275). [8619247] Piscataway: Institute of Electrical and Electronics Engineers. DOI: 10.1109/CDC.2018.8619247

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*2018 IEEE Conference on Decision and Control, CDC 2018.*, 8619247, Institute of Electrical and Electronics Engineers, Piscataway, pp. 270-275, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 17/12/18. DOI: 10.1109/CDC.2018.8619247

**Nyquist stability criteria for control systems with stochastic delays.** / Antunes, Duarte J.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Nyquist stability criteria for control systems with stochastic delays

AU - Antunes,Duarte J.

PY - 2019/1/18

Y1 - 2019/1/18

N2 - We consider a linear control loop with time-varying delays, assumed to be independent and identically distributed random variables following a known probability distribution. We provide Nyquist criteria to assert the convergence to zero of the state statistical moments. The criterion pertaining to the first order moments parallels the one for deterministic time-invariant control loops. In particular, one can determine gain and phase margins. This criterion can be used to assert almost sure stability for positive linear systems. The criterion for the second order moments can be used to assert mean square stability for general linear systems. The applicability of the results is illustrated through a numerical example.

AB - We consider a linear control loop with time-varying delays, assumed to be independent and identically distributed random variables following a known probability distribution. We provide Nyquist criteria to assert the convergence to zero of the state statistical moments. The criterion pertaining to the first order moments parallels the one for deterministic time-invariant control loops. In particular, one can determine gain and phase margins. This criterion can be used to assert almost sure stability for positive linear systems. The criterion for the second order moments can be used to assert mean square stability for general linear systems. The applicability of the results is illustrated through a numerical example.

UR - http://www.scopus.com/inward/record.url?scp=85062175002&partnerID=8YFLogxK

U2 - 10.1109/CDC.2018.8619247

DO - 10.1109/CDC.2018.8619247

M3 - Conference contribution

SN - 978-1-5386-1396-2

SP - 270

EP - 275

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

ER -