### Abstract

In this article, resilient delay-dependent adaptive control algorithms are developed for closed-loop stabilization of a class of uncertain time-delay systems with time-varying state delay, nonlinear dynamical perturbation, and controller gain perturbation. The norm of the nonlinear perturbation is assumed to be bounded by a weighted norm of the state, and the norm of the uncertainty of the state feedback gain is assumed to be bounded by a positive constant. Two main problems are investigated. In the first problem, an adaptive control scheme is developed to guarantee asymptotic stabilization of the closed-loop system when the value of the upper bound of the norm of the state feedback gain perturbation is known. In the second problem, asymptotically stabilizing adaptive controller is derived when the value of the upper bound of the norm of the state feedback gain perturbation is assumed to be unknown. A numerical simulation example, that illustrates the two design approaches, is presented.

Original language | English |
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Title of host publication | Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC |

Pages | 909-914 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2007 |

Event | 46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States Duration: 12 Dec 2007 → 14 Dec 2007 |

### Other

Other | 46th IEEE Conference on Decision and Control 2007, CDC |
---|---|

Country | United States |

City | New Orleans, LA |

Period | 12/12/07 → 14/12/07 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Modelling and Simulation
- Control and Optimization

### Cite this

*Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC*(pp. 909-914). [4434271] https://doi.org/10.1109/CDC.2007.4434271

**Resilient delay-dependent adaptive control of uncertain time-delay systems.** / Nounou, Hazem; Nounou, Mohamed.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC.*, 4434271, pp. 909-914, 46th IEEE Conference on Decision and Control 2007, CDC, New Orleans, LA, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434271

}

TY - GEN

T1 - Resilient delay-dependent adaptive control of uncertain time-delay systems

AU - Nounou, Hazem

AU - Nounou, Mohamed

PY - 2007

Y1 - 2007

N2 - In this article, resilient delay-dependent adaptive control algorithms are developed for closed-loop stabilization of a class of uncertain time-delay systems with time-varying state delay, nonlinear dynamical perturbation, and controller gain perturbation. The norm of the nonlinear perturbation is assumed to be bounded by a weighted norm of the state, and the norm of the uncertainty of the state feedback gain is assumed to be bounded by a positive constant. Two main problems are investigated. In the first problem, an adaptive control scheme is developed to guarantee asymptotic stabilization of the closed-loop system when the value of the upper bound of the norm of the state feedback gain perturbation is known. In the second problem, asymptotically stabilizing adaptive controller is derived when the value of the upper bound of the norm of the state feedback gain perturbation is assumed to be unknown. A numerical simulation example, that illustrates the two design approaches, is presented.

AB - In this article, resilient delay-dependent adaptive control algorithms are developed for closed-loop stabilization of a class of uncertain time-delay systems with time-varying state delay, nonlinear dynamical perturbation, and controller gain perturbation. The norm of the nonlinear perturbation is assumed to be bounded by a weighted norm of the state, and the norm of the uncertainty of the state feedback gain is assumed to be bounded by a positive constant. Two main problems are investigated. In the first problem, an adaptive control scheme is developed to guarantee asymptotic stabilization of the closed-loop system when the value of the upper bound of the norm of the state feedback gain perturbation is known. In the second problem, asymptotically stabilizing adaptive controller is derived when the value of the upper bound of the norm of the state feedback gain perturbation is assumed to be unknown. A numerical simulation example, that illustrates the two design approaches, is presented.

UR - http://www.scopus.com/inward/record.url?scp=62749207144&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62749207144&partnerID=8YFLogxK

U2 - 10.1109/CDC.2007.4434271

DO - 10.1109/CDC.2007.4434271

M3 - Conference contribution

SN - 1424414989

SN - 9781424414987

SP - 909

EP - 914

BT - Proceedings of the 46th IEEE Conference on Decision and Control 2007, CDC

ER -