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Robust and non-fragile finite-time H∞ control for uncertain Markovian jump nonlinear systems

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  • Zhang, Yingqi
  • Shi, Yan
  • Shi, Peng

Abstract

This paper investigates the non-fragile and robust finite-time H∞ control problem for a class of uncertain Markovian jump nonlinear systems with bounded parametric uncertainties and norm-bounded disturbance. By employing stochastic analysis and linear matrix inequality techniques, sufficient criteria of stochastic finite-time boundedness and stochastic H∞ finite-time boundedness are first provided for the class of stochastic jump systems. Then, a controller is designed such that the class of stochastic nonlinear dynamics are stochastically finite-time bounded and have an H∞ attention performance level by utilizing matrix decomposition approach. Furthermore, the analysis and design of non-fragile and robust finite-time controller are provided to guarantee that the class of uncertain stochastic systems are stochastically finite-time boundeded with a prescribed attention index by using non-fragile control technique. In addition, we also deal with the analysis and design of stochastic finite-time stability and stochastic finite-time stabilization. All criterions can be characterized in terms of linear matrix inequalities. Finally, two examples are also given to illustrate the effectiveness of obtained results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:279:y:2016:i:c:p:125-138
    DOI: 10.1016/j.amc.2016.01.012
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    Cited by:

    1. Shu, Feng & Li, Min & Liu, Duyu, 2019. "Non-fragile H∞ control for Markovian jump fuzzy systems with time-varying delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1177-1191.
    2. 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.
    3. Rathinasamy Sakthivel & Ramalingam Sakthivel & Boomipalagan Kaviarasan & Chao Wang & Yong-Ki Ma, 2018. "Finite-Time Nonfragile Synchronization of Stochastic Complex Dynamical Networks with Semi-Markov Switching Outer Coupling," Complexity, Hindawi, vol. 2018, pages 1-13, January.
    4. Li, Lingchun & Shen, Mouquan & Zhang, Guangming & Yan, Shen, 2017. "H∞ control of Markov jump systems with time-varying delay and incomplete transition probabilities," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 95-106.
    5. Wu, Kai-Ning & Sun, Han-Xiao & Yang, Baoqing & Lim, Cheng-Chew, 2018. "Finite-time boundary control for delay reaction–diffusion systems," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 52-63.
    6. Karthick, S.A. & Sakthivel, R. & Ma, Y.K. & Leelamani, A., 2020. "Observer based guaranteed cost control for Markovian jump stochastic neutral-type neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    7. Zhai, Ding & Lu, An-Yang & Dong, Jiuxiang & Zhang, Qing-Ling, 2016. "Asynchronous H∞ filtering for 2D discrete Markovian jump systems with sensor failure," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 60-79.

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