### Abstract

We study the notion of network realizability which is the property of a system to be expressed as sub-systems interacting over a given network. In this paper, we consider the problem of finding an optimal network-realizable controller that can stabilize a networked plant while minimizing the H _{2} norm of the closed-loop transfer function under the constraint that both plant and controller are linear networked systems interacting over a given directed delay network. We extend the notion of network realizability from [1], [2] to systems over a broader class of delay networks and analyze the structure of network realizable systems. Using these structural properties, we characterize the set of all stabilizing controllers that are realizable over the given delay network using the Youla parametrization. The H_{2} control problem is then cast as a convex optimization problem and its solution is shown to provide the optimal distributed controller over the given delay network. The results of this paper allow one to model, analyze and design systems over arbitrary directed delay networks.

Original language | English (US) |
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Title of host publication | 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 7746-7751 |

Number of pages | 6 |

ISBN (Print) | 9781467357173 |

DOIs | |

State | Published - Jan 1 2013 |

Externally published | Yes |

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

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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ISSN (Print) | 0191-2216 |

### 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

### Cite this

*2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013*(pp. 7746-7751). [6761119] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6761119

**Optimal distributed controllers realizable over any arbitrary delay Networks.** / Vamsi, Andalam Satya Mohan; Elia, Nicola.

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

*2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013.*, 6761119, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 7746-7751, 52nd IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, 12/10/13. https://doi.org/10.1109/CDC.2013.6761119

}

TY - GEN

T1 - Optimal distributed controllers realizable over any arbitrary delay Networks

AU - Vamsi, Andalam Satya Mohan

AU - Elia, Nicola

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We study the notion of network realizability which is the property of a system to be expressed as sub-systems interacting over a given network. In this paper, we consider the problem of finding an optimal network-realizable controller that can stabilize a networked plant while minimizing the H 2 norm of the closed-loop transfer function under the constraint that both plant and controller are linear networked systems interacting over a given directed delay network. We extend the notion of network realizability from [1], [2] to systems over a broader class of delay networks and analyze the structure of network realizable systems. Using these structural properties, we characterize the set of all stabilizing controllers that are realizable over the given delay network using the Youla parametrization. The H2 control problem is then cast as a convex optimization problem and its solution is shown to provide the optimal distributed controller over the given delay network. The results of this paper allow one to model, analyze and design systems over arbitrary directed delay networks.

AB - We study the notion of network realizability which is the property of a system to be expressed as sub-systems interacting over a given network. In this paper, we consider the problem of finding an optimal network-realizable controller that can stabilize a networked plant while minimizing the H 2 norm of the closed-loop transfer function under the constraint that both plant and controller are linear networked systems interacting over a given directed delay network. We extend the notion of network realizability from [1], [2] to systems over a broader class of delay networks and analyze the structure of network realizable systems. Using these structural properties, we characterize the set of all stabilizing controllers that are realizable over the given delay network using the Youla parametrization. The H2 control problem is then cast as a convex optimization problem and its solution is shown to provide the optimal distributed controller over the given delay network. The results of this paper allow one to model, analyze and design systems over arbitrary directed delay networks.

UR - http://www.scopus.com/inward/record.url?scp=84902336463&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902336463&partnerID=8YFLogxK

U2 - 10.1109/CDC.2013.6761119

DO - 10.1109/CDC.2013.6761119

M3 - Conference contribution

AN - SCOPUS:84902336463

SN - 9781467357173

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 7746

EP - 7751

BT - 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013

PB - Institute of Electrical and Electronics Engineers Inc.

ER -