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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA17-03224S" target="_blank" >GA17-03224S: Asymptotická teorie obyčejných diferenciálních rovnic celočíselných a neceločíselných řádů a jejich numerických diskretizací</a><br>

Návaznosti

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

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

PHYSICA D-NONLINEAR PHENOMENA

ISSN

0167-2789

e-ISSN

1872-8022

Svazek periodika

404

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

30

Strana od-do

1-30

Kód UT WoS článku

000528248900009

EID výsledku v databázi Scopus

2-s2.0-85078248706