# Large Deviations in Discrete-time Systems with Control Signal Delay

### Nina Vunder, Natalia Dudarenko, Valery Grigoriev

#### Abstract

The paper considers a problem of deviations (peak effect) in the free motion of linear discrete stable systems with a control signal delay. The problem consists in structure of eigenvectors of the state matrix. The control signal delay adds additional order to a discrete-time model and leads to the variation of eigenvectors structure and deviation increasing in the free motion of the system. A tracking discrete-time system is a subject of the research. An approach to the modal control law design taking into account the value of delay and the deviation is suggested in the paper. It is proposed to assess the upper bound of peaking processes in the system with the condition number of an eigenvectors matrix. The results are supported by an example.

Download#### Paper Citation

#### in Harvard Style

Vunder N., Dudarenko N. and Grigoriev V. (2019). **Large Deviations in Discrete-time Systems with Control Signal Delay**.In *Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-758-380-3, pages 281-288. DOI: 10.5220/0007920702810288

#### in Bibtex Style

@conference{icinco19,

author={Nina Vunder and Natalia Dudarenko and Valery Grigoriev},

title={Large Deviations in Discrete-time Systems with Control Signal Delay},

booktitle={Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2019},

pages={281-288},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007920702810288},

isbn={978-989-758-380-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - Large Deviations in Discrete-time Systems with Control Signal Delay

SN - 978-989-758-380-3

AU - Vunder N.

AU - Dudarenko N.

AU - Grigoriev V.

PY - 2019

SP - 281

EP - 288

DO - 10.5220/0007920702810288