### Abstract

This paper deals with the design of state-feedback delay-dependent H 8 controller for active vibration control problem of seismic-excited structures having actuator delay, L 2 disturbances and actuator saturation. First sufficient delay-dependent criteria are developed by choosing a Lyapunov-Krasovskii functional candidate for a stabilizing H 8 synthesis involving a matrix inequality conditions. Then actuator saturation phenomenon is added to the controller design using LMI constraints. The sufficient conditions for designing such controller are obtained in terms of delay-dependent bilinear matrix inequalities (BMIs). To overcome nonlinear optimization problem involved in the delay-dependent conditions, a cone complementary linearization method is used to find a feasible solution set. Using proposed method, a suboptimal controller with maximum allowable delay bound, minimum allowable disturbance attenuation level under actuator saturation constraints can be obtained simultaneously by a convex optimization technique. A four-degree-of-freedom structural system subject to Kobe Earthquake excitations is used to illustrate the effectiveness of the approach through simulations. Simulation results show that the proposed controller is very effective in reducing vibration amplitudes of storeys and guarantees stability at maximum actuator delay bound under actuator saturation constraints.

Original language | Undefined/Unknown |
---|---|

Title of host publication | Vibration Problems ICOVP 2011 |

Subtitle of host publication | The 10th International Conference on Vibration Problems |

Editors | Jiri Naprstek, Jaromir Horacek, Miloslav Okrouhlik, Bohdana Marvalova, Ferdinand Verhulst, Jerzy T Sawicki |

Publisher | Springer |

Pages | 413-418 |

Number of pages | 6 |

ISBN (Electronic) | 9789400720695 |

ISBN (Print) | 9789400720688 |

DOIs | |

Publication status | Published - Dec 2011 |

### Publication series

Name | Springer Proceedings In Physics |
---|---|

Publisher | Springer Netherlands |

Number | 139 |

### Keywords

- active vibration control
- H8 control
- actuator delay
- actuator saturation
- linear matrix inequalities

## Cite this

Yazici, H., Guclu, R., & Kucukdemiral, I. B. (2011). Siesmic vibration attenuation of a structural system having actuator saturation with a delay dependent H infinity controller. In J. Naprstek, J. Horacek, M. Okrouhlik, B. Marvalova, F. Verhulst, & J. T. Sawicki (Eds.),

*Vibration Problems ICOVP 2011: The 10th International Conference on Vibration Problems*(pp. 413-418). (Springer Proceedings In Physics; No. 139). Springer. https://doi.org/10.1007/978-94-007-2069-5_56