On the attainability of an estimate of a number of Perron exponents for discrete linear diagonal systems with bounded coefficients

Alexander Konyukh; Michal Niezabitowski

doi:10.1109/MMAR.2015.7284014

On the attainability of an estimate of a number of Perron exponents for discrete linear diagonal systems with bounded coefficients

Alexander Konyukh
, Michal Niezabitowski

Department of Automatic Control and Robotics (RAU/RAU3)

Belarus State Economic University
Silesian University of Technology

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

7 Citations (Scopus)

Abstract

The Lyapunov, Perron and Bohl exponents are the most important numerical characteristics of dynamic systems used in control theory. Properties of the first one are well investigated. Properties of the Perron and Bohl exponents are much less described in the literature, for example the questions about the structure of the sets of values of these quantities for general discrete-time systems are still open. In this paper we give an example of a two-dimensional system with bounded coefficients that have three different Perron exponents. In addition, we prove that the s-dimensional diagonal discrete-time system with bounded coefficients can have any number of different Perron exponents between 1 and 2^s - 1.

Original language	English
Title of host publication	2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	994-999
Number of pages	6
ISBN (Electronic)	9781479987016
DOIs	https://doi.org/10.1109/MMAR.2015.7284014
Publication status	Published - 29 Sept 2015
Event	20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015 - Miedzyzdroje, Poland Duration: 24 Aug 2015 → 27 Aug 2015

Publication series

Name	2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015

Conference

Conference	20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015
Country/Territory	Poland
City	Miedzyzdroje
Period	24/08/15 → 27/08/15

Keywords

Lyapunov exponent
Perron exponent
diagonal discrete time-varying systems

ASJC Scopus subject areas

Artificial Intelligence
Computer Vision and Pattern Recognition
Control and Systems Engineering

Access to Document

10.1109/MMAR.2015.7284014

Cite this

Konyukh, A., & Niezabitowski, M. (2015). On the attainability of an estimate of a number of Perron exponents for discrete linear diagonal systems with bounded coefficients. In 2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015 (pp. 994-999). Article 7284014 (2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/MMAR.2015.7284014

Konyukh, Alexander ; Niezabitowski, Michal. / On the attainability of an estimate of a number of Perron exponents for discrete linear diagonal systems with bounded coefficients. 2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 994-999 (2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015).

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title = "On the attainability of an estimate of a number of Perron exponents for discrete linear diagonal systems with bounded coefficients",

abstract = "The Lyapunov, Perron and Bohl exponents are the most important numerical characteristics of dynamic systems used in control theory. Properties of the first one are well investigated. Properties of the Perron and Bohl exponents are much less described in the literature, for example the questions about the structure of the sets of values of these quantities for general discrete-time systems are still open. In this paper we give an example of a two-dimensional system with bounded coefficients that have three different Perron exponents. In addition, we prove that the s-dimensional diagonal discrete-time system with bounded coefficients can have any number of different Perron exponents between 1 and 2s - 1.",

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Konyukh, A & Niezabitowski, M 2015, On the attainability of an estimate of a number of Perron exponents for discrete linear diagonal systems with bounded coefficients. in 2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015., 7284014, 2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015, Institute of Electrical and Electronics Engineers Inc., pp. 994-999, 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015, Miedzyzdroje, Poland, 24/08/15. https://doi.org/10.1109/MMAR.2015.7284014

On the attainability of an estimate of a number of Perron exponents for discrete linear diagonal systems with bounded coefficients. / Konyukh, Alexander; Niezabitowski, Michal.
2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 994-999 7284014 (2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015).

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

TY - GEN

T1 - On the attainability of an estimate of a number of Perron exponents for discrete linear diagonal systems with bounded coefficients

AU - Konyukh, Alexander

AU - Niezabitowski, Michal

PY - 2015/9/29

Y1 - 2015/9/29

N2 - The Lyapunov, Perron and Bohl exponents are the most important numerical characteristics of dynamic systems used in control theory. Properties of the first one are well investigated. Properties of the Perron and Bohl exponents are much less described in the literature, for example the questions about the structure of the sets of values of these quantities for general discrete-time systems are still open. In this paper we give an example of a two-dimensional system with bounded coefficients that have three different Perron exponents. In addition, we prove that the s-dimensional diagonal discrete-time system with bounded coefficients can have any number of different Perron exponents between 1 and 2s - 1.

AB - The Lyapunov, Perron and Bohl exponents are the most important numerical characteristics of dynamic systems used in control theory. Properties of the first one are well investigated. Properties of the Perron and Bohl exponents are much less described in the literature, for example the questions about the structure of the sets of values of these quantities for general discrete-time systems are still open. In this paper we give an example of a two-dimensional system with bounded coefficients that have three different Perron exponents. In addition, we prove that the s-dimensional diagonal discrete-time system with bounded coefficients can have any number of different Perron exponents between 1 and 2s - 1.

KW - Lyapunov exponent

KW - Perron exponent

KW - diagonal discrete time-varying systems

UR - https://www.scopus.com/pages/publications/84964499531

U2 - 10.1109/MMAR.2015.7284014

DO - 10.1109/MMAR.2015.7284014

M3 - Conference contribution

AN - SCOPUS:84964499531

T3 - 2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015

SP - 994

EP - 999

BT - 2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015

Y2 - 24 August 2015 through 27 August 2015

ER -

Konyukh A, Niezabitowski M. On the attainability of an estimate of a number of Perron exponents for discrete linear diagonal systems with bounded coefficients. In 2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015. Institute of Electrical and Electronics Engineers Inc. 2015. p. 994-999. 7284014. (2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015). doi: 10.1109/MMAR.2015.7284014

On the attainability of an estimate of a number of Perron exponents for discrete linear diagonal systems with bounded coefficients

Abstract

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