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Dissipativity based repetitive control for switched stochastic dynamical systems

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  • Sakthivel, R.
  • Saravanakumar, T.
  • Kaviarasan, B.
  • Marshal Anthoni, S.

Abstract

This paper addresses the issues of dissipativity analysis and repetitive control synthesis for a class of switched stochastic dynamical systems with time-varying delay. By using the lifting technique, the considered one dimensional model is converted into a continuous-discrete stochastic two dimensional delayed model to describe the control and learning actions of the repetitive controller. By employing stochastic system theory together with Lyapunov function technique, a new set of sufficient conditions in terms of linear matrix inequalities (LMIs) is established such that the switched stochastic system in two dimensional delayed model is mean square asymptotically stable and (Q,S,R)-dissipative. Then, the desired repetitive controller is designed by solving a convex optimization problem established in terms of LMIs. More precisely, repetitive controllers with H∞, passivity and mixed H∞ and passivity performances can be obtained as the special cases for the considered system. Finally, numerical examples are provided to demonstrate the effectiveness and potential of the developed design technique.

Suggested Citation

  • Sakthivel, R. & Saravanakumar, T. & Kaviarasan, B. & Marshal Anthoni, S., 2016. "Dissipativity based repetitive control for switched stochastic dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 340-353.
    • Handle: RePEc:eee:apmaco:v:291:y:2016:i:c:p:340-353
    DOI: 10.1016/j.amc.2016.07.019
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    References listed on IDEAS

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    1. Wang, Guoliang, 2015. "Stochastic stabilization of singular systems with Markovian switchings," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 390-401.
    2. Zhiguang Feng & James Lam & Zhan Shu, 2013. "Dissipative control for linear systems by static output feedback," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(8), pages 1566-1576.
    3. Sakthivel, R. & Rathika, M. & Santra, Srimanta & Zhu, Quanxin, 2015. "Dissipative reliable controller design for uncertain systems and its application," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 107-121.
    4. Qi, Wenhai & Gao, Xianwen, 2016. "H∞ observer design for stochastic time-delayed systems with Markovian switching under partly known transition rates and actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 80-97.
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    Cited by:

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    2. Shen, Mouquan & Ye, Dan, 2017. "A finite frequency approach to control of Markov jump linear systems with incomplete transition probabilities," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 53-64.
    3. Georgiou, F. & Thamwattana, N., 2020. "Modelling phagocytosis based on cell–cell adhesion and prey–predator relationship," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 52-64.
    4. Yang, Chengyu & Li, Fei & Kong, Qingkai & Chen, Xiangyong & Wang, Jian, 2021. "Asynchronous fault-tolerant control for stochastic jumping singularly perturbed systems: An H∞ sliding mode control scheme," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    5. Deng, Yalin & Zhang, Huasheng & Dai, Yuzhen & Li, Yuanen, 2022. "Interval stability/stabilization for linear stochastic switched systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 428(C).

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