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Stochastic stability of switching linear systems with application to an automotive powertrain model

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  • Vargas, Alessandro N.
  • Caruntu, Constantin F.
  • Ishihara, João Y.
  • Bouzahir, Hassane

Abstract

This paper presents a simple-to-check stability condition for switching linear systems driven by stochastic switching signals. The stability concept under investigation is known as the mean-square asymptotic stability. The main assumption is that the switching intervals form independent, identically distributed random processes. Under this assumption, the stability condition requires checking the spectral radius of certain matrices. The effectiveness of the stability result is illustrated through an automotive powertrain model. Data from the automotive powertrain simulator support the theoretical findings.

Suggested Citation

  • Vargas, Alessandro N. & Caruntu, Constantin F. & Ishihara, João Y. & Bouzahir, Hassane, 2022. "Stochastic stability of switching linear systems with application to an automotive powertrain model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 278-287.
    • Handle: RePEc:eee:matcom:v:191:y:2022:i:c:p:278-287
    DOI: 10.1016/j.matcom.2021.08.006
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    References listed on IDEAS

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    1. Buckwar, Evelyn & Sickenberger, Thorsten, 2011. "A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1110-1127.
    2. Wang, Huajian & Qi, Wenhai & Zhang, Lihua & Cheng, Jun & Kao, Yonggui, 2020. "Stability and stabilization for positive systems with semi-Markov switching," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    3. Matcovschi, Mihaela-Hanako & Pastravanu, Octavian, 2012. "Diagonally invariant exponential stability and stabilizability of switching linear systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1407-1418.
    4. Zhang, Yingqi & Shi, Yan & Shi, Peng, 2016. "Robust and non-fragile finite-time H∞ control for uncertain Markovian jump nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 125-138.
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