### Abstract

This paper considers a decentralized ℋ_{2} control problem for multichannel linear time-invariant (LTI) descriptor systems. Our interest is to design a low order dynamic output feedback controller. The control problem is reduced to a feasibility problem of a bilinear matrix inequality (BMI) with respect to variables of a coefficient matrix defining the controller, a Lyapunov matrix and a matrix related to the descriptor matrix. Under a matching condition between the descriptor matrix and the measurement output matrix (or the control input matrix), we propose to set the Lyapunov matrix in the BMI as block diagonal appropriately so that the BMI is reduced to LMIs.

Original language | English |
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Title of host publication | Proceedings of the 16th IFAC World Congress, IFAC 2005 |

Publisher | IFAC Secretariat |

Pages | 51-56 |

Number of pages | 6 |

ISBN (Print) | 008045108X, 9780080451084 |

DOIs | |

Publication status | Published - 2005 Jan 1 |

### Publication series

Name | IFAC Proceedings Volumes (IFAC-PapersOnline) |
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Volume | 16 |

ISSN (Print) | 1474-6670 |

### Keywords

- Bilinear matrix inequality (BMI)
- Decentralized control
- Linear matrix inequality (LMI)
- Multi-channel descriptor system

### ASJC Scopus subject areas

- Control and Systems Engineering

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## Cite this

_{2}controller design for descriptor systems: An LMI approach. In

*Proceedings of the 16th IFAC World Congress, IFAC 2005*(pp. 51-56). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 16). IFAC Secretariat. https://doi.org/10.3182/20050703-6-cz-1902.01549