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Robust stability of stochastic systems with varying delays: Application to RLC circuit with intermittent closed-loop

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  • Hamdi, Issam El
  • Vargas, Alessandro N.
  • Bouzahir, Hassane
  • Oliveira, Ricardo C.L.F.
  • Acho, Leonardo

Abstract

This paper characterizes the robust second-moment stability of stochastic linear systems subject to varying delays. The delays assume a particular form suitable to represent packet loss in networked control systems, under the zero-order hold feedback. The proposed robust stability condition requires checking the spectral radius of an appropriate matrix that that depends on uncertain parameters belonging to a polytope. Due to this polytope’s dependence, checking the spectral radius is difficult from the numerical viewpoint. As an attempt to solve the problem, we convert the polytope-based condition into a randomized approach. Namely, we present probability bounds that help us certificate the robust second-moment stability under high probability. A real-time electronic application illustrates the potential benefits of our approach.

Suggested Citation

  • Hamdi, Issam El & Vargas, Alessandro N. & Bouzahir, Hassane & Oliveira, Ricardo C.L.F. & Acho, Leonardo, 2021. "Robust stability of stochastic systems with varying delays: Application to RLC circuit with intermittent closed-loop," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    • Handle: RePEc:eee:apmaco:v:411:y:2021:i:c:s0096300321006251
    DOI: 10.1016/j.amc.2021.126541
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    References listed on IDEAS

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    1. Li, Zhi-Min & Chang, Xiao-Heng & Yu, Lu, 2016. "Robust quantized H∞ filtering for discrete-time uncertain systems with packet dropouts," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 361-371.
    2. Vargas, Alessandro N. & Montezuma, Marcio A.F. & Liu, Xinghua & Oliveira, Ricardo C.L.F., 2019. "Robust stability of Markov jump linear systems through randomized evaluations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 287-294.
    3. Haghighi, Payam & Tavassoli, Babak & Farhadi, Alireza, 2020. "A practical approach to networked control design for robust H∞ performance in the presence of uncertainties in both communication and system," Applied Mathematics and Computation, Elsevier, vol. 381(C).
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