Eigenvalue Based Approach for Assessment of Global Robustness of Nonlinear Dynamical Systems

Eigenvalue Based Approach for Assessment of Global Robustness of Nonlinear Dynamical Systems

In this paper we have established the sufficient conditions for asymptotic convergence of all solutions of nonlinear dynamical system (with potentially unknown and unbounded external disturbances) to zero with time <inline-formula> <math display="inline"> <semantics> <...

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Main Author: Robert Vrabel
Format: Article
Language:English
Published: MDPI AG 2019-04-01
Series:Symmetry
Subjects:
nonlinear system
perturbation
robustness
variation of constants formula
symmetric part of linear operator
Online Access:https://www.mdpi.com/2073-8994/11/4/569
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spelling doaj-1066b16783044895a47a4dd7d374613d2020-11-24T21:49:08ZengMDPI AGSymmetry2073-89942019-04-0111456910.3390/sym11040569sym11040569Eigenvalue Based Approach for Assessment of Global Robustness of Nonlinear Dynamical SystemsRobert Vrabel0Institute of Applied Informatics, Automation and Mechatronics, Slovak University of Technology in Bratislava, Bottova 25, 917 01 Trnava, SlovakiaIn this paper we have established the sufficient conditions for asymptotic convergence of all solutions of nonlinear dynamical system (with potentially unknown and unbounded external disturbances) to zero with time <inline-formula> <math display="inline"> <semantics> <mrow> <mi>t</mi> <mo>&#8594;</mo> <mo>&#8734;</mo> <mo>.</mo> </mrow> </semantics> </math> </inline-formula> We showed here that the symmetric part of linear part of nonlinear nominal system, or, to be more precise, its time-dependent eigenvalues, play important role in assessment of the robustness of systems.https://www.mdpi.com/2073-8994/11/4/569nonlinear systemperturbationrobustnessvariation of constants formulasymmetric part of linear operator
collection DOAJ
language English
format Article
sources DOAJ
author Robert Vrabel
spellingShingle Robert Vrabel
Eigenvalue Based Approach for Assessment of Global Robustness of Nonlinear Dynamical Systems
Symmetry
nonlinear system
perturbation
robustness
variation of constants formula
symmetric part of linear operator
author_facet Robert Vrabel
author_sort Robert Vrabel
title Eigenvalue Based Approach for Assessment of Global Robustness of Nonlinear Dynamical Systems
title_short Eigenvalue Based Approach for Assessment of Global Robustness of Nonlinear Dynamical Systems
title_full Eigenvalue Based Approach for Assessment of Global Robustness of Nonlinear Dynamical Systems
title_fullStr Eigenvalue Based Approach for Assessment of Global Robustness of Nonlinear Dynamical Systems
title_full_unstemmed Eigenvalue Based Approach for Assessment of Global Robustness of Nonlinear Dynamical Systems
title_sort eigenvalue based approach for assessment of global robustness of nonlinear dynamical systems
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2019-04-01
description In this paper we have established the sufficient conditions for asymptotic convergence of all solutions of nonlinear dynamical system (with potentially unknown and unbounded external disturbances) to zero with time <inline-formula> <math display="inline"> <semantics> <mrow> <mi>t</mi> <mo>&#8594;</mo> <mo>&#8734;</mo> <mo>.</mo> </mrow> </semantics> </math> </inline-formula> We showed here that the symmetric part of linear part of nonlinear nominal system, or, to be more precise, its time-dependent eigenvalues, play important role in assessment of the robustness of systems.
topic nonlinear system
perturbation
robustness
variation of constants formula
symmetric part of linear operator
url https://www.mdpi.com/2073-8994/11/4/569
work_keys_str_mv AT robertvrabel eigenvaluebasedapproachforassessmentofglobalrobustnessofnonlineardynamicalsystems
_version_ 1725889357047398400

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