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Stochastic admissibility of singular Markov jump systems driven by fractional Brownian motion based on SMC technology

Author

Listed:
  • Zhou, Xia
  • He, Pengzhi
  • Ding, Yiting
  • Cheng, Jun
  • Li, Kezan

Abstract

The stochastic admissibility problem of singular Markov jump systems (SMJSs) driven by fractional Brownian motion (FBM) with time-varying delay is studied based on sliding mode control (SMC) technology. To address the non-Markovian and non-martingale properties of FBM, as well as the complexities arising from the singularity of SMJSs, modal jumps, and time-varying delay, a novel Lyapunov–Krasovskii functional with a delay-integral term is constructed, and an integral sliding mode surface (SMS) incorporating Markovian jump modes is designed, and a fractional infinitesimal operator that includes the Hurst exponent H is established, and then sufficient conditions in the form of linear matrix inequalities are derived to guarantee that the closed-loop system is regular, impulse-free, and stochastically stable. Furthermore, a corresponding SMC law is designed, and it is rigorously proven that the system states can reach the SMS within a finite time. Finally, a numerical example is provided to verify the correctness and effectiveness of the proposed theoretical method.

Suggested Citation

  • Zhou, Xia & He, Pengzhi & Ding, Yiting & Cheng, Jun & Li, Kezan, 2026. "Stochastic admissibility of singular Markov jump systems driven by fractional Brownian motion based on SMC technology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 694(C).
    • Handle: RePEc:eee:phsmap:v:694:y:2026:i:c:s0378437125009161
    DOI: 10.1016/j.physa.2025.131264
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