### Abstract

We focus on the positive definiteness in the linear matrix inequality (LMI) problem obtained from H _{∞} output feedback control problem. In particular, we provide a necessary condition for an inequality constraint of the LMI problem, which is called the coupling constraint, to strictly hold at optimal solutions. It is reasonable to expect that the condition does not hold for most generalized plants. In other words, the strict inequality at the optimal solutions rarely happens in H _{∞} output feedback control for most generalized plants. Thus, we must apply remedies for constructing a controller after solving the LMI problem.

Original language | English |
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Article number | 8637724 |

Pages (from-to) | 446-451 |

Number of pages | 6 |

Journal | IEEE Control Systems Letters |

Volume | 3 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 1 2019 |

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### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Control and Optimization

### Cite this

**Positive Definiteness in Linear Matrix Inequality Problem for H-Infinity Output Feedback Control Problem.** / Waki, Hayato.

Research output: Contribution to journal › Article

*IEEE Control Systems Letters*, vol. 3, no. 2, 8637724, pp. 446-451. https://doi.org/10.1109/LCSYS.2019.2898385

}

TY - JOUR

T1 - Positive Definiteness in Linear Matrix Inequality Problem for H-Infinity Output Feedback Control Problem

AU - Waki, Hayato

PY - 2019/4/1

Y1 - 2019/4/1

N2 - We focus on the positive definiteness in the linear matrix inequality (LMI) problem obtained from H ∞ output feedback control problem. In particular, we provide a necessary condition for an inequality constraint of the LMI problem, which is called the coupling constraint, to strictly hold at optimal solutions. It is reasonable to expect that the condition does not hold for most generalized plants. In other words, the strict inequality at the optimal solutions rarely happens in H ∞ output feedback control for most generalized plants. Thus, we must apply remedies for constructing a controller after solving the LMI problem.

AB - We focus on the positive definiteness in the linear matrix inequality (LMI) problem obtained from H ∞ output feedback control problem. In particular, we provide a necessary condition for an inequality constraint of the LMI problem, which is called the coupling constraint, to strictly hold at optimal solutions. It is reasonable to expect that the condition does not hold for most generalized plants. In other words, the strict inequality at the optimal solutions rarely happens in H ∞ output feedback control for most generalized plants. Thus, we must apply remedies for constructing a controller after solving the LMI problem.

UR - http://www.scopus.com/inward/record.url?scp=85061550039&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061550039&partnerID=8YFLogxK

U2 - 10.1109/LCSYS.2019.2898385

DO - 10.1109/LCSYS.2019.2898385

M3 - Article

AN - SCOPUS:85061550039

VL - 3

SP - 446

EP - 451

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

SN - 2475-1456

IS - 2

M1 - 8637724

ER -