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Stability Assessment of Stochastic Differential-Algebraic Systems via Lyapunov Exponents with an Application to Power Systems

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Stability Assessment of Stochastic Differential-Algebraic Systems via Lyapunov Exponents with an Application to Power Systems

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dc.contributor.author González-Zumba, Andrés es_ES
dc.contributor.author Fernández de Córdoba, Pedro es_ES
dc.contributor.author Cortés, J.-C. es_ES
dc.contributor.author Mehrmann, Volker es_ES
dc.date.accessioned 2021-09-10T03:30:57Z
dc.date.available 2021-09-10T03:30:57Z
dc.date.issued 2020-09 es_ES
dc.identifier.uri http://hdl.handle.net/10251/172001
dc.description.abstract [EN] In this paper, we discuss stochastic differential-algebraic equations (SDAEs) and the asymptotic stability assessment for such systems via Lyapunov exponents (LEs). We focus on index-1 SDAEs and their reformulation as ordinary stochastic differential equations (SDEs). Via ergodic theory, it is then feasible to analyze the LEs via the random dynamical system generated by the underlying SDEs. Once the existence of well-defined LEs is guaranteed, we proceed to the use of numerical simulation techniques to determine the LEs numerically. Discrete and continuous QR decomposition-based numerical methods are implemented to compute the fundamental solution matrix and to use it in the computation of the LEs. Important computational features of both methods are illustrated via numerical tests. Finally, the methods are applied to two applications from power systems engineering, including the single-machine infinite-bus (SMIB) power system model. es_ES
dc.description.sponsorship A.G.-Z. was supported by Secretaria Nacional de Ciencia y Tecnologia SENESCYT (Ecuador), through the scholarship "Becas de Fomento al Talento Humano", and Deutsche Forschungsgemeinschaft through Collaborative Research Centre Transregio. SFB TRR 154. P.F.-d.-C. was partially supported by grant no. RTI2018-102256-B-I00 (Spain). J.-C.C. acknowledges the support by the Spanish Ministerio de Economia, Industria y Competitividad (MINECO), the Agencia Estatal de Investigacion (AEI), and Fondo Europeo de Desarrollo Regional (FEDER UE) grant MTM2017-89664-P. V.M. was partially supported by Deutsche Forschungsgemeinschaft through the Excellence Cluster Math+ in Berlin, and Priority Program 1984 "Hybride und multimodale Energiesysteme: Systemtheoretische Methoden fur die Transformation und den Betrieb komplexer Netze". es_ES
dc.language Inglés es_ES
dc.publisher MDPI AG es_ES
dc.relation.ispartof Mathematics es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Stochastic differential-algebraic equations es_ES
dc.subject Lyapunov exponent es_ES
dc.subject Power system stability es_ES
dc.subject Spectral analysis es_ES
dc.subject Stochastic systems es_ES
dc.subject Numerical methods es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Stability Assessment of Stochastic Differential-Algebraic Systems via Lyapunov Exponents with an Application to Power Systems es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3390/math8091393 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/DFG//SFB TRR 154/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-89664-P/ES/PROBLEMAS DINAMICOS CON INCERTIDUMBRE SIMULABLE: MODELIZACION MATEMATICA, ANALISIS, COMPUTACION Y APLICACIONES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/RTI2018-102256-B-I00/ES/TRANSFERENCIA DE CALOR EN FLUJOS DE PARED: CANALES Y CAPAS LIMITES/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation González-Zumba, A.; Fernández De Córdoba, P.; Cortés, J.; Mehrmann, V. (2020). Stability Assessment of Stochastic Differential-Algebraic Systems via Lyapunov Exponents with an Application to Power Systems. Mathematics. 8(9):1-26. https://doi.org/10.3390/math8091393 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3390/math8091393 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 26 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 8 es_ES
dc.description.issue 9 es_ES
dc.identifier.eissn 2227-7390 es_ES
dc.relation.pasarela S\417210 es_ES
dc.contributor.funder Deutsche Forschungsgemeinschaft es_ES
dc.contributor.funder AGENCIA ESTATAL DE INVESTIGACION es_ES
dc.contributor.funder European Regional Development Fund es_ES
dc.contributor.funder Secretaría de Educación Superior, Ciencia, Tecnología e Innovación, Ecuador es_ES
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