Lyapunov Spectra Behavior for Linear Time-Varying Discrete Systems Under Small Perturbations

Adam Czornik; Evgenii K. Makarov; Michal Niezabitowski; Svetlana Popova; Vasilii Zaitsev

doi:10.1109/ACCESS.2022.3189566

Lyapunov Spectra Behavior for Linear Time-Varying Discrete Systems Under Small Perturbations

Adam Czornik
, Evgenii K. Makarov
, Michal Niezabitowski
, Svetlana Popova
, Vasilii Zaitsev

Department of Automatic Control and Robotics (RAU/RAU3)

Belarus Academy of Sciences
Udmurt State University

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the behavior of the Lyapunov spectrum of a linear time-varying discrete system under the action of small perturbations in order to obtain some verifiable conditions for stability and openness of the Lyapunov spectrum. To this end we introduce the concepts of broken away solutions and splitted systems. The main results obtained are a necessary condition for stability and a sufficient condition for the openness of the Lyapunov spectrum, which is given in terms of the system itself. Finally, examples of using the obtained results are presented.

Original language	English
Pages (from-to)	74779-74791
Number of pages	13
Journal	IEEE Access
Volume	10
DOIs	https://doi.org/10.1109/ACCESS.2022.3189566
Publication status	Published - 2022

Keywords

Linear time-varying discrete systems
Lyapunov spectrum
multiplicative perturbations
small perturbations

ASJC Scopus subject areas

General Computer Science
General Materials Science
General Engineering

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10.1109/ACCESS.2022.3189566

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title = "Lyapunov Spectra Behavior for Linear Time-Varying Discrete Systems Under Small Perturbations",

abstract = "We investigate the behavior of the Lyapunov spectrum of a linear time-varying discrete system under the action of small perturbations in order to obtain some verifiable conditions for stability and openness of the Lyapunov spectrum. To this end we introduce the concepts of broken away solutions and splitted systems. The main results obtained are a necessary condition for stability and a sufficient condition for the openness of the Lyapunov spectrum, which is given in terms of the system itself. Finally, examples of using the obtained results are presented.",

keywords = "Linear time-varying discrete systems, Lyapunov spectrum, multiplicative perturbations, small perturbations",

author = "Adam Czornik and Makarov, \{Evgenii K.\} and Michal Niezabitowski and Svetlana Popova and Vasilii Zaitsev",

note = "Publisher Copyright: {\textcopyright} 2013 IEEE.",

year = "2022",

doi = "10.1109/ACCESS.2022.3189566",

language = "English",

volume = "10",

pages = "74779--74791",

journal = "IEEE Access",

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T1 - Lyapunov Spectra Behavior for Linear Time-Varying Discrete Systems Under Small Perturbations

AU - Czornik, Adam

AU - Makarov, Evgenii K.

AU - Niezabitowski, Michal

AU - Popova, Svetlana

AU - Zaitsev, Vasilii

PY - 2022

Y1 - 2022

N2 - We investigate the behavior of the Lyapunov spectrum of a linear time-varying discrete system under the action of small perturbations in order to obtain some verifiable conditions for stability and openness of the Lyapunov spectrum. To this end we introduce the concepts of broken away solutions and splitted systems. The main results obtained are a necessary condition for stability and a sufficient condition for the openness of the Lyapunov spectrum, which is given in terms of the system itself. Finally, examples of using the obtained results are presented.

AB - We investigate the behavior of the Lyapunov spectrum of a linear time-varying discrete system under the action of small perturbations in order to obtain some verifiable conditions for stability and openness of the Lyapunov spectrum. To this end we introduce the concepts of broken away solutions and splitted systems. The main results obtained are a necessary condition for stability and a sufficient condition for the openness of the Lyapunov spectrum, which is given in terms of the system itself. Finally, examples of using the obtained results are presented.

KW - Linear time-varying discrete systems

KW - Lyapunov spectrum

KW - multiplicative perturbations

KW - small perturbations

UR - https://www.scopus.com/pages/publications/85134249208

U2 - 10.1109/ACCESS.2022.3189566

DO - 10.1109/ACCESS.2022.3189566

M3 - Article

AN - SCOPUS:85134249208

SN - 2169-3536

VL - 10

SP - 74779

EP - 74791

JO - IEEE Access

JF - IEEE Access

ER -

Lyapunov Spectra Behavior for Linear Time-Varying Discrete Systems Under Small Perturbations

Abstract

Keywords

ASJC Scopus subject areas

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