# Freezing Method Approach to an Asymptotic Stability of the Discrete-time Oscillator Equation

### Artur Babiarz, Adam Czornik, Michal Niezabitowski

#### Abstract

The presented research work considers stability criteria of second-order differential equation. The second-order discrete-time oscillator equation is obtained from discretization of second order continuous-time equation using the forward difference operator. The stability criteria are drawn with freezing method and are presented in the terms of the equation coefficients. Finally, an illustrative example is shown.

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#### Paper Citation

#### in Harvard Style

Babiarz A., Czornik A. and Niezabitowski M. (2015). **Freezing Method Approach to an Asymptotic Stability of the Discrete-time Oscillator Equation** . In *Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-758-122-9, pages 353-357. DOI: 10.5220/0005512903530357

#### in Bibtex Style

@conference{icinco15,

author={Artur Babiarz and Adam Czornik and Michal Niezabitowski},

title={Freezing Method Approach to an Asymptotic Stability of the Discrete-time Oscillator Equation},

booktitle={Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2015},

pages={353-357},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005512903530357},

isbn={978-989-758-122-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - Freezing Method Approach to an Asymptotic Stability of the Discrete-time Oscillator Equation

SN - 978-989-758-122-9

AU - Babiarz A.

AU - Czornik A.

AU - Niezabitowski M.

PY - 2015

SP - 353

EP - 357

DO - 10.5220/0005512903530357