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A design of fuzzy sliding mode control for Markovian jumping system with different input matrices

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  • Zhang, Jianyu
  • Wang, Yingying
  • Yang, Songwei
  • Li, Jiaojiao
  • Qu, Hao

Abstract

In this paper, by means of sliding mode control (SMC), the problem resulted by local input matrices is investigated for fuzzy markovian jumping system. The stability of the considered fuzzy Markovian system with multiple sub-input matrices can be fulfilled using the method in this paper. First, the state equation of the considered system is transformed according to the input matrices. Second, according to the state equation, sliding mode surface is constructed. This surface contains several sub-surfaces. It can deal with this kind of fuzzy Markovian system with multiple sub-input matrices and uncertainties. And another characteristic is that there is not the process of reaching the sliding mode surface; It can settle the problem resulted by Markovian jumping and sliding mode method together. Third, by use of the Cramer's rule, a criterion is provided to judge the existence of sliding mode dynamics equation. A controller containing several sub-controllers components is designed. And these sub-controllers should keep the considered system on the several sub-surfaces and not leave it. At last, simulations are provided to illustrate the validity of the method in this paper.

Suggested Citation

  • Zhang, Jianyu & Wang, Yingying & Yang, Songwei & Li, Jiaojiao & Qu, Hao, 2024. "A design of fuzzy sliding mode control for Markovian jumping system with different input matrices," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    • Handle: RePEc:eee:apmaco:v:463:y:2024:i:c:s0096300323005416
    DOI: 10.1016/j.amc.2023.128372
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    References listed on IDEAS

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    1. Dong, Jiuxiang & Hou, Junteng, 2017. "Output feedback fault-tolerant control by a set-theoretic description of T–S fuzzy systems," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 117-134.
    2. Liang, Tiantian & Shi, Shengli & Ma, Yuechao, 2023. "Asynchronous sliding mode control of continuous-time singular markov jump systems with time-varying delay under event-triggered strategy," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    3. Feng, Bo & Feng, Zhiguang & Li, Peng, 2023. "Improved results on reachable set synthesis of Markovian jump systems with time-varying delays: General asynchronous control approaches," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    4. Liu, Mingyu & Xie, Jing & Kao, Yonggui, 2023. "Stochastic bounded consensus for multi-agent systems with fractional Brownian motions via sliding mode control," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    5. Zeghlache, Samir & Ghellab, Mohammed Zinelaabidine & Djerioui, Ali & Bouderah, Brahim & Benkhoris, Mohamed Fouad, 2023. "Adaptive fuzzy fast terminal sliding mode control for inverted pendulum-cart system with actuator faults," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 207-234.
    6. Mao, Xuerong, 1999. "Stability of stochastic differential equations with Markovian switching," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 45-67, January.
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