Stability/Instability Study and Control of Autonomous Dynamical Systems: Divergence Method

Stability/Instability Study and Control of Autonomous Dynamical Systems: Divergence Method

A novel method of instability and stability study of equilibrium points of autonomous dynamical systems using a flow and divergence of the vector field is proposed. A relation between the Lyapunov, Gauss (Ostrogradsky) and Chetaev theorems with the divergence ones is established. The generalizations...

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Main Authors: Igor B. Furtat, Pavel A. Gushchin
Format: Article
Language:English
Published: IEEE 2021-01-01
Series:IEEE Access
Subjects:
Autonomous system
control
divergence
flow of the vector field
instability
periodic solution
Online Access:https://ieeexplore.ieee.org/document/9345693/
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spelling doaj-7befc20d0ebf4ba0828fb7e64a7d9f9b2021-03-30T15:07:27ZengIEEEIEEE Access2169-35362021-01-019237642377110.1109/ACCESS.2021.30569429345693Stability/Instability Study and Control of Autonomous Dynamical Systems: Divergence MethodIgor B. Furtat0https://orcid.org/0000-0003-4679-5884Pavel A. Gushchin1Institute for Problems~in Mechanical Engineering of the Russian Academy of Sciences (IPME RAS), St. Petersburg, RussiaInstitute for Problems~in Mechanical Engineering of the Russian Academy of Sciences (IPME RAS), St. Petersburg, RussiaA novel method of instability and stability study of equilibrium points of autonomous dynamical systems using a flow and divergence of the vector field is proposed. A relation between the Lyapunov, Gauss (Ostrogradsky) and Chetaev theorems with the divergence ones is established. The generalizations of Bendixon and Bendixon-Dulac theorems about a lack of periodic solutions in arbitrary order systems are considered. The state feedback control law design based on new divergence conditions is proposed. Examples illustrate the efficiency of the proposed method and comparisons with some existing ones.https://ieeexplore.ieee.org/document/9345693/Autonomous systemcontroldivergenceflow of the vector fieldinstabilityperiodic solution
collection DOAJ
language English
format Article
sources DOAJ
author Igor B. Furtat
Pavel A. Gushchin
spellingShingle Igor B. Furtat
Pavel A. Gushchin
Stability/Instability Study and Control of Autonomous Dynamical Systems: Divergence Method
IEEE Access
Autonomous system
control
divergence
flow of the vector field
instability
periodic solution
author_facet Igor B. Furtat
Pavel A. Gushchin
author_sort Igor B. Furtat
title Stability/Instability Study and Control of Autonomous Dynamical Systems: Divergence Method
title_short Stability/Instability Study and Control of Autonomous Dynamical Systems: Divergence Method
title_full Stability/Instability Study and Control of Autonomous Dynamical Systems: Divergence Method
title_fullStr Stability/Instability Study and Control of Autonomous Dynamical Systems: Divergence Method
title_full_unstemmed Stability/Instability Study and Control of Autonomous Dynamical Systems: Divergence Method
title_sort stability/instability study and control of autonomous dynamical systems: divergence method
publisher IEEE
series IEEE Access
issn 2169-3536
publishDate 2021-01-01
description A novel method of instability and stability study of equilibrium points of autonomous dynamical systems using a flow and divergence of the vector field is proposed. A relation between the Lyapunov, Gauss (Ostrogradsky) and Chetaev theorems with the divergence ones is established. The generalizations of Bendixon and Bendixon-Dulac theorems about a lack of periodic solutions in arbitrary order systems are considered. The state feedback control law design based on new divergence conditions is proposed. Examples illustrate the efficiency of the proposed method and comparisons with some existing ones.
topic Autonomous system
control
divergence
flow of the vector field
instability
periodic solution
url https://ieeexplore.ieee.org/document/9345693/
work_keys_str_mv AT igorbfurtat stabilityinstabilitystudyandcontrolofautonomousdynamicalsystemsdivergencemethod
AT pavelagushchin stabilityinstabilitystudyandcontrolofautonomousdynamicalsystemsdivergencemethod
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