### Abstract

This paper is focused on the l_{2}-induced control of eventually periodic linear discrete-time systems. We prove for such systems that a synthesis exists if and only if an eventually periodic synthesis exists. We also consider specific cases, where we show that the synthesis if existent can always be chosen to be of the same eventually periodic class as the plant. All the conditions derived are provided in terms of semi-definite programming problems. The motivation for this work is controlling nonlinear systems along prespecified trajectories, notably those which eventually settle down into periodic orbits and those with uncertain initial states.

Original language | English (US) |
---|---|

Pages (from-to) | 2021-2026 |

Number of pages | 6 |

Journal | Proceedings of the American Control Conference |

Volume | 3 |

State | Published - Nov 29 2004 |

Event | Proceedings of the 2004 American Control Conference (AAC) - Boston, MA, United States Duration: Jun 30 2004 → Jul 2 2004 |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

_{2}-induced control for eventually periodic systems.

*Proceedings of the American Control Conference*,

*3*, 2021-2026.

**On the l _{2}-induced control for eventually periodic systems.** / Farhood, Mazen; Dullerud, Geir E.

Research output: Contribution to journal › Conference article

_{2}-induced control for eventually periodic systems',

*Proceedings of the American Control Conference*, vol. 3, pp. 2021-2026.

_{2}-induced control for eventually periodic systems. Proceedings of the American Control Conference. 2004 Nov 29;3:2021-2026.

}

TY - JOUR

T1 - On the l2-induced control for eventually periodic systems

AU - Farhood, Mazen

AU - Dullerud, Geir E

PY - 2004/11/29

Y1 - 2004/11/29

N2 - This paper is focused on the l2-induced control of eventually periodic linear discrete-time systems. We prove for such systems that a synthesis exists if and only if an eventually periodic synthesis exists. We also consider specific cases, where we show that the synthesis if existent can always be chosen to be of the same eventually periodic class as the plant. All the conditions derived are provided in terms of semi-definite programming problems. The motivation for this work is controlling nonlinear systems along prespecified trajectories, notably those which eventually settle down into periodic orbits and those with uncertain initial states.

AB - This paper is focused on the l2-induced control of eventually periodic linear discrete-time systems. We prove for such systems that a synthesis exists if and only if an eventually periodic synthesis exists. We also consider specific cases, where we show that the synthesis if existent can always be chosen to be of the same eventually periodic class as the plant. All the conditions derived are provided in terms of semi-definite programming problems. The motivation for this work is controlling nonlinear systems along prespecified trajectories, notably those which eventually settle down into periodic orbits and those with uncertain initial states.

UR - http://www.scopus.com/inward/record.url?scp=8744291810&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=8744291810&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:8744291810

VL - 3

SP - 2021

EP - 2026

JO - Proceedings of the American Control Conference

JF - Proceedings of the American Control Conference

SN - 0743-1619

ER -