### Abstract

This paper considers an analysis and synthesis problem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops an Linear Matrix Inequality (LMI) approach. First, we present an existence condition and an explicit formula of controllers, which guarantee a prescribed level of L^{2} gain of closed loop systems, in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for the cases of delay-independent/dependent and memoryless/memory controllers, while the infinity dimensionality of the LMIs makes the result difficult to apply. Second, we introduce a technique to reduce the infinite-dimensional LMIs to a finite number of LMIs, and present a feasible algorithm for synthesis of controllers based on the finite-dimensional LMIs.

Original language | English |
---|---|

Pages (from-to) | 505-520 |

Number of pages | 16 |

Journal | Kybernetika |

Volume | 37 |

Issue number | 4 |

Publication status | Published - 2001 |

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### ASJC Scopus subject areas

- Human-Computer Interaction
- Control and Systems Engineering

### Cite this

*Kybernetika*,

*37*(4), 505-520.

**Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems.** / Ikeda, Kojiro; Azuma, Takehito; Uchida, Kenko.

Research output: Contribution to journal › Article

*Kybernetika*, vol. 37, no. 4, pp. 505-520.

}

TY - JOUR

T1 - Infinite-dimensional LMI approach to analysis and synthesis for linear time-delay systems

AU - Ikeda, Kojiro

AU - Azuma, Takehito

AU - Uchida, Kenko

PY - 2001

Y1 - 2001

N2 - This paper considers an analysis and synthesis problem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops an Linear Matrix Inequality (LMI) approach. First, we present an existence condition and an explicit formula of controllers, which guarantee a prescribed level of L2 gain of closed loop systems, in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for the cases of delay-independent/dependent and memoryless/memory controllers, while the infinity dimensionality of the LMIs makes the result difficult to apply. Second, we introduce a technique to reduce the infinite-dimensional LMIs to a finite number of LMIs, and present a feasible algorithm for synthesis of controllers based on the finite-dimensional LMIs.

AB - This paper considers an analysis and synthesis problem of controllers for linear time-delay systems in the form of delay-dependent memory state feedback, and develops an Linear Matrix Inequality (LMI) approach. First, we present an existence condition and an explicit formula of controllers, which guarantee a prescribed level of L2 gain of closed loop systems, in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for the cases of delay-independent/dependent and memoryless/memory controllers, while the infinity dimensionality of the LMIs makes the result difficult to apply. Second, we introduce a technique to reduce the infinite-dimensional LMIs to a finite number of LMIs, and present a feasible algorithm for synthesis of controllers based on the finite-dimensional LMIs.

UR - http://www.scopus.com/inward/record.url?scp=0035648514&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035648514&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0035648514

VL - 37

SP - 505

EP - 520

JO - Kybernetika

JF - Kybernetika

SN - 0023-5954

IS - 4

ER -