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Determining Asymptotic Stability and Robustness of Networked Systems

Determining Asymptotic Stability and Robustness of Networked Systems

Title: Determining Asymptotic Stability and Robustness of Networked Systems
Author: August, Elias   orcid.org/0000-0001-9018-5624
Date: 2020-10-29
Language: English
Scope: 39
University/Institute: Háskólinn í Reykjavík
Reykjavik University
School: Tæknisvið (HR)
School of Technology (RU)
Department: Verkfræðideild (HR)
Department of Engineering (RU)
Series: Systems;8(4)
ISSN: 2079-8954 (eISSN)
DOI: 10.3390/systems8040039
Subject: Coupled nonlinear systems; Stability; Robustness; Semidefinite programming; Sum of squares decomposition; Continuous stirred tank reactor; Tölvunet; Kraftur; Jafnvægi; Reiknilíkön; Forritun
URI: https://hdl.handle.net/20.500.11815/2525

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August, E. (2020). Determining Asymptotic Stability and Robustness of Networked Systems. Systems, 8(4), 39. https://doi.org/10.3390/systems8040039


This paper is motivated by the notion that coupling systems allows for mitigating the failure of individual ones. We present a novel approach to determining asymptotic stability and robustness of a network consisting of coupled dynamical systems, where individual system dynamics are represented through polynomial or rational functions. The analysis relies on a local analysis; thus, making it computationally implementable. We present an efficient computational method that relies on semidefinite programming. Importantly, for cases where multiple equilibrium points exist, we show how to determine regions around an asymptotically stable equilibrium point that bounds solutions. These regions increase when systems are coupled as we observe when applying the presented analysis framework to a mathematical model of a continuous stirred tank reactor. Importantly, the presented work has implications to other fields as well.


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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution(CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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