On stabilization of unstable steady states of autonomous ordinary differential equations via delayed feedback controls

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F20%3APU135771" target="_blank" >RIV/00216305:26210/20:PU135771 - isvavai.cz</a>

Result on the web

<a href="https://www.sciencedirect.com/science/article/pii/S0167278918304834" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0167278918304834</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.physd.2020.132339" target="_blank" >10.1016/j.physd.2020.132339</a>

Result language

angličtina

Original language name

On stabilization of unstable steady states of autonomous ordinary differential equations via delayed feedback controls

Original language description

The paper discusses stabilizing effects of some time-delayed feedback controls applied to unstable steady states of an autonomous system of ordinary differential equations. First, we derive explicit delay-dependent stability conditions that are applicable to a family of time-delayed systems with simultaneously triangularizable system matrices. Then, using this criterion and other argumentation, we employ diagonal delayed feedback controls of conventional and Pyragas type to stabilize unstable steady states of the studied autonomous system. More precisely, we formulate explicit, non-improvable and immediately applicable conditions on time delay and feedback strength that enable such a stabilization. As an illustration, we stabilize the unstable steady states of the Rössler dynamical system considered under the standard choice of entry parameters when the uncontrolled system displays a chaotic behavior. Also, we consider a non-diagonal feedback control (whose rotational gain matrix, involving a feedback strength and phase, commutes with the Jacobi matrix of the uncontrolled system) and show its larger stabilization potential with respect to the appropriate diagonal control. The obtained results are tested by numerical experiments and confronted with the existing results. As a supplement, we provide MATLAB codes supporting theoretical conclusions.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

<a href="/en/project/GA17-03224S" target="_blank" >GA17-03224S: Asymptotic theory of ordinary and fractional differential equations and their numerical discretizations</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2020

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

PHYSICA D-NONLINEAR PHENOMENA

ISSN

0167-2789

e-ISSN

1872-8022

Volume of the periodical

404

Issue of the periodical within the volume

1

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

30

Pages from-to

1-30

UT code for WoS article

000528248900009

EID of the result in the Scopus database

2-s2.0-85078248706