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Stabilization of Takagi–Sugeno fuzzy Hidden Markov Jump Systems with memory sampled-data control

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  • Rakkiyappan, R.
  • Sharmila, V.
  • Janani, K.
  • Kashkynbayev, Ardak

Abstract

The stability of Takagi–Sugeno fuzzy hidden Markovian jump systems by employing a memory sampled-data control (SDC) scheme that includes a constant signal transmission delay is investigated. The asynchronous situation between the system plant and the controller is represented using the hidden Markov model. The stability of the provided model is ensured by implication of the fuzzy time-scheduled Lyapunov functional (LF), and the sufficient conditions are derived in the form of linear matrix inequalities (LMIs). This simplifies the utilization and generalization of the analysis results, as they exhibit convexity in the subsystem matrix. Additionally, it diminishes the influence of external disturbances by employing the H∞ norm bound. To acquire the required time-dependent memory SDC, it is necessary to solve this set of LMIs. The efficacy and feasibility of the proposed method is established by attaining stability for a chaotic Lorenz system using the T–S fuzzy Hidden Markov Jump Systems with Memory SDC.

Suggested Citation

  • Rakkiyappan, R. & Sharmila, V. & Janani, K. & Kashkynbayev, Ardak, 2024. "Stabilization of Takagi–Sugeno fuzzy Hidden Markov Jump Systems with memory sampled-data control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 204-217.
  • Handle: RePEc:eee:matcom:v:226:y:2024:i:c:p:204-217
    DOI: 10.1016/j.matcom.2024.07.015
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    References listed on IDEAS

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    1. Guo, Beibei & Xiao, Yu, 2024. "Synchronization of multi-link and multi-delayed inertial neural networks with Markov jump via aperiodically intermittent adaptive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 435-453.
    2. Zhang, Ziyu & Yang, Xinsong & Lam, Hak-Keung & Xiang, Zhengrong, 2024. "Event-triggered control for switched systems with sensor faults via adaptive fuzzy observer," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 244-259.
    3. Houda, K. & Saifia, D. & Chadli, M. & Labiod, S., 2023. "Unknown input observer based robust control for fuzzy descriptor systems subject to actuator saturation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 150-173.
    4. Tian, Yufeng & Wang, Yuzhong & Ren, Junchao, 2020. "Stability analysis and control design of singular Markovian jump systems via a parameter-dependent reciprocally convex matrix inequality," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    5. Zeng, Hong-Bing & Liu, Xiao-Gui & Wang, Wei, 2019. "A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 1-8.
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