### Abstract

In this paper, we address the problem of identifying fixed order stable SISO systems from time and frequency domain data. Given measurements of time and frequency response corrupted by process and measurement noise, we aim at finding a fixed order stable plant whose response matches the data collected (within the noise bounds) and whose H_{∞} norm is below a prescribed level. It is shown the problem can be solved by finding a point in a set defined by polynomial inequalities and the sparse structure of the polynomials is exploited to develop an efficient system identification algorithm. Further computational improvements are obtained by reformulating the problem as a rank constrained one and using efficient convex relaxations of rank minimization. Numerical examples are provided to illustrate the efficiency of the proposed algorithms.

Original language | English (US) |
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Title of host publication | Proceedings of the 2011 American Control Conference, ACC 2011 |

Pages | 1253-1259 |

Number of pages | 7 |

State | Published - Sep 29 2011 |

Event | 2011 American Control Conference, ACC 2011 - San Francisco, CA, United States Duration: Jun 29 2011 → Jul 1 2011 |

### Publication series

Name | Proceedings of the American Control Conference |
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ISSN (Print) | 0743-1619 |

### Other

Other | 2011 American Control Conference, ACC 2011 |
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Country | United States |

City | San Francisco, CA |

Period | 6/29/11 → 7/1/11 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering

### Cite this

*Proceedings of the 2011 American Control Conference, ACC 2011*(pp. 1253-1259). [5990950] (Proceedings of the American Control Conference).

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*Proceedings of the 2011 American Control Conference, ACC 2011.*, 5990950, Proceedings of the American Control Conference, pp. 1253-1259, 2011 American Control Conference, ACC 2011, San Francisco, CA, United States, 6/29/11.

**Identifying stable fixed order systems from time and frequency response data.** / Feng, C.; Lagoa, Constantino Manuel; Sznaier, M.

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

TY - GEN

T1 - Identifying stable fixed order systems from time and frequency response data

AU - Feng, C.

AU - Lagoa, Constantino Manuel

AU - Sznaier, M.

PY - 2011/9/29

Y1 - 2011/9/29

N2 - In this paper, we address the problem of identifying fixed order stable SISO systems from time and frequency domain data. Given measurements of time and frequency response corrupted by process and measurement noise, we aim at finding a fixed order stable plant whose response matches the data collected (within the noise bounds) and whose H∞ norm is below a prescribed level. It is shown the problem can be solved by finding a point in a set defined by polynomial inequalities and the sparse structure of the polynomials is exploited to develop an efficient system identification algorithm. Further computational improvements are obtained by reformulating the problem as a rank constrained one and using efficient convex relaxations of rank minimization. Numerical examples are provided to illustrate the efficiency of the proposed algorithms.

AB - In this paper, we address the problem of identifying fixed order stable SISO systems from time and frequency domain data. Given measurements of time and frequency response corrupted by process and measurement noise, we aim at finding a fixed order stable plant whose response matches the data collected (within the noise bounds) and whose H∞ norm is below a prescribed level. It is shown the problem can be solved by finding a point in a set defined by polynomial inequalities and the sparse structure of the polynomials is exploited to develop an efficient system identification algorithm. Further computational improvements are obtained by reformulating the problem as a rank constrained one and using efficient convex relaxations of rank minimization. Numerical examples are provided to illustrate the efficiency of the proposed algorithms.

UR - http://www.scopus.com/inward/record.url?scp=80053160284&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053160284&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781457700804

T3 - Proceedings of the American Control Conference

SP - 1253

EP - 1259

BT - Proceedings of the 2011 American Control Conference, ACC 2011

ER -