IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v291y2016icp340-353.html
   My bibliography  Save this article

Dissipativity based repetitive control for switched stochastic dynamical systems

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316304490
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.07.019?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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).
    3. 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).
    4. Sakthivel, R. & Karthick, S.A. & Kaviarasan, B. & Lim, Yongdo, 2017. "Reliable state estimation of switched neutral system with nonlinear actuator faults via sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 129-147.
    5. 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.
    6. Mohanapriya, S. & Crispin Sweety, C. Antony & Satheesh, T. & Sakthivel, R. & Kwon, O.M., 2024. "Modified equivalent input disturbance estimator-based active disturbance rejection for fractional-order T-S fuzzy stochastic systems," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gao, Xianwen & He, Hangfeng & Qi, Wenhai, 2017. "Admissibility analysis for discrete-time singular Markov jump systems with asynchronous switching," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 431-441.
    2. Fu, Lei & Ma, Yuechao, 2016. "Passive control for singular time-delay system with actuator saturation," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 181-193.
    3. Shen, Zixiang & Li, Chuandong & Li, Hongfei & Cao, Zhengran, 2019. "Estimation of the domain of attraction for discrete-time linear impulsive control systems with input saturation," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    4. Sakthivel, R. & Joby, Maya & Wang, Chao & Kaviarasan, B., 2018. "Finite-time fault-tolerant control of neutral systems against actuator saturation and nonlinear actuator faults," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 425-436.
    5. 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).
    6. Wang, Guoliang & Li, Zhiqiang & Zhang, Qingling & Yang, Chunyu, 2017. "Robust finite-time stability and stabilization of uncertain Markovian jump systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 377-393.
    7. Wang, Guoliang & Cai, Hongyang & Zhang, Qingling & Yang, Chunyu, 2017. "Stabilization of stochastic delay systems via a disordered controller," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 98-109.
    8. Zhang, Jie & Sun, Yuangong & Meng, Fanwei, 2020. "State bounding for discrete-time switched nonlinear time-varying systems using ADT method," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    9. Kumar, S. Vimal & Anthoni, S. Marshal & Raja, R., 2019. "Dissipative analysis for aircraft flight control systems with randomly occurring uncertainties via non-fragile sampled-data control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 217-226.
    10. Wang, Huajian & Qi, Wenhai & Zhang, Lihua & Cheng, Jun & Kao, Yonggui, 2020. "Stability and stabilization for positive systems with semi-Markov switching," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    11. Fang, Jiankang & Ren, Chengcheng & Wang, Hai & Stojanovic, Vladimir & He, Shuping, 2024. "Finite-region asynchronous H∞ filtering for 2-D Markov jump systems in Roesser model," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    12. Kwon, Nam Kyu & Park, In Seok & Park, PooGyeon, 2017. "H∞ control for singular Markovian jump systems with incomplete knowledge of transition probabilities," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 126-135.
    13. Nagamani, G. & Ramasamy, S., 2016. "Stochastic dissipativity and passivity analysis for discrete-time neural networks with probabilistic time-varying delays in the leakage term," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 237-257.
    14. Nguyen, Khanh Hieu & Kim, Sung Hyun, 2020. "Observer-based control design of semi-Markovian jump systems with uncertain probability intensities and mode-transition-dependent sojourn-time distribution," Applied Mathematics and Computation, Elsevier, vol. 372(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:291:y:2016:i:c:p:340-353. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.