The relations between the senior upper general exponent and the upper Bohl exponents

Adam Czornik

doi:10.1109/MMAR.2014.6957476

The relations between the senior upper general exponent and the upper Bohl exponents

Adam Czornik

Department of Automatic Control and Robotics (RAU/RAU3)

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

17 Citations (Scopus)

Abstract

The Bohl exponents, similarly to the Lyapunov exponents, are among the most important numerical characteristics of dynamical systems used in control theory. Properties of the Lyapunov characteristics are well described in the literature. Properties of the Bohl exponents are investigated much less. In this paper we consider the so-called senior upper general exponent of a discrete linear time-varying system and present some alternative formulas for it. Moreover, we discuss relations between upper Bohl exponents of the perturbed system and the senior upper general exponent of the unperturbed system.

Original language	English
Title of host publication	2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	897-902
Number of pages	6
ISBN (Electronic)	9781479950812
DOIs	https://doi.org/10.1109/MMAR.2014.6957476
Publication status	Published - 13 Nov 2014
Event	2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014 - Miedzyzdroje, Poland Duration: 2 Sept 2014 → 5 Sept 2014

Publication series

Name	2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014

Conference

Conference	2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014
Country/Territory	Poland
City	Miedzyzdroje
Period	2/09/14 → 5/09/14

Keywords

Lyapunov exponent
perturbed system
senior upper general exponent
stability of linear systems
time-varying systems
upper Bohl exponents

ASJC Scopus subject areas

Artificial Intelligence
Human-Computer Interaction

Access to Document

10.1109/MMAR.2014.6957476

Cite this

Czornik, A. (2014). The relations between the senior upper general exponent and the upper Bohl exponents. In 2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014 (pp. 897-902). Article 6957476 (2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/MMAR.2014.6957476

Czornik, Adam. / The relations between the senior upper general exponent and the upper Bohl exponents. 2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014. Institute of Electrical and Electronics Engineers Inc., 2014. pp. 897-902 (2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014).

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abstract = "The Bohl exponents, similarly to the Lyapunov exponents, are among the most important numerical characteristics of dynamical systems used in control theory. Properties of the Lyapunov characteristics are well described in the literature. Properties of the Bohl exponents are investigated much less. In this paper we consider the so-called senior upper general exponent of a discrete linear time-varying system and present some alternative formulas for it. Moreover, we discuss relations between upper Bohl exponents of the perturbed system and the senior upper general exponent of the unperturbed system.",

keywords = "Lyapunov exponent, perturbed system, senior upper general exponent, stability of linear systems, time-varying systems, upper Bohl exponents",

author = "Adam Czornik",

note = "Publisher Copyright: {\textcopyright} 2014 IEEE.; 2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014 ; Conference date: 02-09-2014 Through 05-09-2014",

year = "2014",

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language = "English",

series = "2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014",

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Czornik, A 2014, The relations between the senior upper general exponent and the upper Bohl exponents. in 2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014., 6957476, 2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014, Institute of Electrical and Electronics Engineers Inc., pp. 897-902, 2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014, Miedzyzdroje, Poland, 2/09/14. https://doi.org/10.1109/MMAR.2014.6957476

The relations between the senior upper general exponent and the upper Bohl exponents. / Czornik, Adam.
2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014. Institute of Electrical and Electronics Engineers Inc., 2014. p. 897-902 6957476 (2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014).

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

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AU - Czornik, Adam

PY - 2014/11/13

Y1 - 2014/11/13

N2 - The Bohl exponents, similarly to the Lyapunov exponents, are among the most important numerical characteristics of dynamical systems used in control theory. Properties of the Lyapunov characteristics are well described in the literature. Properties of the Bohl exponents are investigated much less. In this paper we consider the so-called senior upper general exponent of a discrete linear time-varying system and present some alternative formulas for it. Moreover, we discuss relations between upper Bohl exponents of the perturbed system and the senior upper general exponent of the unperturbed system.

AB - The Bohl exponents, similarly to the Lyapunov exponents, are among the most important numerical characteristics of dynamical systems used in control theory. Properties of the Lyapunov characteristics are well described in the literature. Properties of the Bohl exponents are investigated much less. In this paper we consider the so-called senior upper general exponent of a discrete linear time-varying system and present some alternative formulas for it. Moreover, we discuss relations between upper Bohl exponents of the perturbed system and the senior upper general exponent of the unperturbed system.

KW - Lyapunov exponent

KW - perturbed system

KW - senior upper general exponent

KW - stability of linear systems

KW - time-varying systems

KW - upper Bohl exponents

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DO - 10.1109/MMAR.2014.6957476

M3 - Conference contribution

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BT - 2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014

Y2 - 2 September 2014 through 5 September 2014

ER -

Czornik A. The relations between the senior upper general exponent and the upper Bohl exponents. In 2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014. Institute of Electrical and Electronics Engineers Inc. 2014. p. 897-902. 6957476. (2014 19th International Conference on Methods and Models in Automation and Robotics, MMAR 2014). doi: 10.1109/MMAR.2014.6957476

The relations between the senior upper general exponent and the upper Bohl exponents

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