# On the Asymptotic Stability Analysis of a Certain Type of Discrete-time 3-D Linear Systems

### Guido Izuta

#### Abstract

This work is concerned with the analysis of 3-d (3-dimensional) systems. The aim is to establish conditions that guarantee the asymptotic stability of these kinds of systems. To accomplish it, the Lagrange candidate solutions method for partial difference equations is adopted here. We show that the systems are asymptotically stable if the entries of the matrices of their state space descriptions yield a solution in the Lagrange solution sense. Furthermore, the particular cases in which the matrices can be turned into a diagonal matrix by means of the canonical transformation is studied in order to figure out the role of the eigenvalues on the stability conditions.

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#### Paper Citation

#### in Harvard Style

Izuta G. (2014). **On the Asymptotic Stability Analysis of a Certain Type of Discrete-time 3-D Linear Systems** . In *Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,* ISBN 978-989-758-039-0, pages 665-670. DOI: 10.5220/0005043306650670

#### in Bibtex Style

@conference{icinco14,

author={Guido Izuta},

title={On the Asymptotic Stability Analysis of a Certain Type of Discrete-time 3-D Linear Systems},

booktitle={Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

year={2014},

pages={665-670},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005043306650670},

isbn={978-989-758-039-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,

TI - On the Asymptotic Stability Analysis of a Certain Type of Discrete-time 3-D Linear Systems

SN - 978-989-758-039-0

AU - Izuta G.

PY - 2014

SP - 665

EP - 670

DO - 10.5220/0005043306650670