### Abstract

In this note, we address two design problems for Linear Parameter-Varying (LPV) systems; Gain-Scheduled (GS) H_{2} state-feedback controller design and GS H_{∞} state-feedback controller design. In sharp contrast to the methods in the literature, the scheduling parameters are supposed to be inexactly measured. The LPV systems are supposed to have polynomially parameter-dependent statespace matrices, and the controllers to be designed are supposed to be rationally parameter-dependent. Using a parametrically affine matrix, which is the inverse of Lyapunov variable, we give formulations for the design of GS H_{2} and H_{∞} state-feedback controllers which are robust against the uncertainties in the measured scheduling parameters, in terms of parametrically affine Linear Matrix Inequalities (LMIs). As a special case, our methods include robust controller design using constant Lyapunov variables. Simple numerical examples are included to illustrate our results.

Original language | English |
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Title of host publication | Proceedings of the 2010 American Control Conference, ACC 2010 |

Pages | 3094-3099 |

Number of pages | 6 |

Publication status | Published - Oct 15 2010 |

Externally published | Yes |

Event | 2010 American Control Conference, ACC 2010 - Baltimore, MD, United States Duration: Jun 30 2010 → Jul 2 2010 |

### Publication series

Name | Proceedings of the 2010 American Control Conference, ACC 2010 |
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### Conference

Conference | 2010 American Control Conference, ACC 2010 |
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Country | United States |

City | Baltimore, MD |

Period | 6/30/10 → 7/2/10 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering

### Cite this

_{2}and H

_{∞}problems. In

*Proceedings of the 2010 American Control Conference, ACC 2010*(pp. 3094-3099). [5531145] (Proceedings of the 2010 American Control Conference, ACC 2010).

**Gain-Scheduled state-feedback controllers using inexactly measured scheduling parameters : H _{2} and H_{∞} problems.** / Sato, Masayuki; Ebihara, Yoshio; Peaucelle, Dimitri.

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

_{2}and H

_{∞}problems. in

*Proceedings of the 2010 American Control Conference, ACC 2010.*, 5531145, Proceedings of the 2010 American Control Conference, ACC 2010, pp. 3094-3099, 2010 American Control Conference, ACC 2010, Baltimore, MD, United States, 6/30/10.

_{2}and H

_{∞}problems. In Proceedings of the 2010 American Control Conference, ACC 2010. 2010. p. 3094-3099. 5531145. (Proceedings of the 2010 American Control Conference, ACC 2010).

}

TY - GEN

T1 - Gain-Scheduled state-feedback controllers using inexactly measured scheduling parameters

T2 - H2 and H∞ problems

AU - Sato, Masayuki

AU - Ebihara, Yoshio

AU - Peaucelle, Dimitri

PY - 2010/10/15

Y1 - 2010/10/15

N2 - In this note, we address two design problems for Linear Parameter-Varying (LPV) systems; Gain-Scheduled (GS) H2 state-feedback controller design and GS H∞ state-feedback controller design. In sharp contrast to the methods in the literature, the scheduling parameters are supposed to be inexactly measured. The LPV systems are supposed to have polynomially parameter-dependent statespace matrices, and the controllers to be designed are supposed to be rationally parameter-dependent. Using a parametrically affine matrix, which is the inverse of Lyapunov variable, we give formulations for the design of GS H2 and H∞ state-feedback controllers which are robust against the uncertainties in the measured scheduling parameters, in terms of parametrically affine Linear Matrix Inequalities (LMIs). As a special case, our methods include robust controller design using constant Lyapunov variables. Simple numerical examples are included to illustrate our results.

AB - In this note, we address two design problems for Linear Parameter-Varying (LPV) systems; Gain-Scheduled (GS) H2 state-feedback controller design and GS H∞ state-feedback controller design. In sharp contrast to the methods in the literature, the scheduling parameters are supposed to be inexactly measured. The LPV systems are supposed to have polynomially parameter-dependent statespace matrices, and the controllers to be designed are supposed to be rationally parameter-dependent. Using a parametrically affine matrix, which is the inverse of Lyapunov variable, we give formulations for the design of GS H2 and H∞ state-feedback controllers which are robust against the uncertainties in the measured scheduling parameters, in terms of parametrically affine Linear Matrix Inequalities (LMIs). As a special case, our methods include robust controller design using constant Lyapunov variables. Simple numerical examples are included to illustrate our results.

UR - http://www.scopus.com/inward/record.url?scp=77957798187&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957798187&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:77957798187

SN - 9781424474264

T3 - Proceedings of the 2010 American Control Conference, ACC 2010

SP - 3094

EP - 3099

BT - Proceedings of the 2010 American Control Conference, ACC 2010

ER -