### Abstract

The paper presents new results for the robust guaranteed cost control problem for a nonlinear neutral system having infinite delay with a given quadratic cost function. A delay dependent stability criterion, based on a model transformation technique, is proposed. A state feedback control law is then designed using the Razumikhin stability approach and the Lyapunov matrix equation to ensure not only the closed-loop systems robust stability but guarantee that the closed-loop cost function value remains within a specified bound. The problem of designing the optimal guaranteed cost controller is also given in terms of inequalities. An example illustrates the theoretical results.

Original language | English |
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Title of host publication | 2015 European Control Conference (ECC) |

Publisher | IEEE |

Pages | 1255 - 1260 |

ISBN (Print) | 9781467371605 |

DOIs | |

Publication status | Published - 2015 |

Event | 2015 European Control Conference - Linz, Austria Duration: 15 Jul 2015 → 17 Jul 2015 |

### Conference

Conference | 2015 European Control Conference |
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Abbreviated title | ECC |

Country | Austria |

City | Linz |

Period | 15/07/15 → 17/07/15 |

### Bibliographical note

The full text is not available on the repository.### Keywords

- Lyapunov matrix equations
- closed loop systems
- control system synthesis
- delays
- nonlinear control systems
- optimal control
- robust control
- state feedback
- Lyapunov matrix equation
- Razumikhin stability approach
- closed-loop cost function value
- delay dependent stability criterion
- infinite delay
- model transformation technique
- nonlinear neutral system
- optimal guaranteed cost controller design
- quadratic cost function
- robust guaranteed cost control
- state feedback control law
- Cost function
- Delays
- Linear matrix inequalities
- Mathematical model
- Robustness
- Stability criteria

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## Cite this

Davies, I., & Haas, O. L. C. (2015). Robust guaranteed cost control for a nonlinear neutral system with infinite delay. In

*2015 European Control Conference (ECC)*(pp. 1255 - 1260). IEEE. https://doi.org/10.1109/ECC.2015.7330712