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Open AccessArticle

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

1
Departamento de Matemática Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
2
Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
3
Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
4
Institut für Mathematik MA 4-5, Technische Universität Berlin, Str. des 17. Juni 136, D-10623 Berlin, Germany
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(9), 1393; https://doi.org/10.3390/math8091393
Received: 24 July 2020 / Revised: 14 August 2020 / Accepted: 18 August 2020 / Published: 20 August 2020
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 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. View Full-Text
Keywords: stochastic differential-algebraic equations; lyapunov exponent; power system stability; spectral analysis; stochastic systems; numerical methods stochastic differential-algebraic equations; lyapunov exponent; power system stability; spectral analysis; stochastic systems; numerical methods
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MDPI and ACS Style

González-Zumba, A.; Fernández-de-Córdoba, P.; Cortés, J.-C.; Mehrmann, V. Stability Assessment of Stochastic Differential-Algebraic Systems via Lyapunov Exponents with an Application to Power Systems. Mathematics 2020, 8, 1393. https://doi.org/10.3390/math8091393

AMA Style

González-Zumba A, Fernández-de-Córdoba P, Cortés J-C, Mehrmann V. Stability Assessment of Stochastic Differential-Algebraic Systems via Lyapunov Exponents with an Application to Power Systems. Mathematics. 2020; 8(9):1393. https://doi.org/10.3390/math8091393

Chicago/Turabian Style

González-Zumba, Andrés; Fernández-de-Córdoba, Pedro; Cortés, Juan-Carlos; Mehrmann, Volker. 2020. "Stability Assessment of Stochastic Differential-Algebraic Systems via Lyapunov Exponents with an Application to Power Systems" Mathematics 8, no. 9: 1393. https://doi.org/10.3390/math8091393

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