A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Advanced Search
Volume 6 Issue 6
Nov.  2019

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 15.3, Top 1 (SCI Q1)
    CiteScore: 23.5, Top 2% (Q1)
    Google Scholar h5-index: 77， TOP 5
Turn off MathJax
Article Contents
Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2019  >  6(6): 1499-1505
Yan Zhang, Ke Lou and Yuan Ge, "New Result on Delay-dependent Stability for Markovian Jump Time-delay Systems With Partial Information on Transition Probabilities," IEEE/CAA J. Autom. Sinica, vol. 6, no. 6, pp. 1499-1505, Nov. 2019. doi: 10.1109/JAS.2016.7510229
Citation: Yan Zhang, Ke Lou and Yuan Ge, "New Result on Delay-dependent Stability for Markovian Jump Time-delay Systems With Partial Information on Transition Probabilities," IEEE/CAA J. Autom. Sinica, vol. 6, no. 6, pp. 1499-1505, Nov. 2019. doi: 10.1109/JAS.2016.7510229
shu

New Result on Delay-dependent Stability for Markovian Jump Time-delay Systems With Partial Information on Transition Probabilities

doi: 10.1109/JAS.2016.7510229

  • College of Electrical Engineering, Anhui Key Laboratory of Detection Technology and Energy Saving Devices, Anhui Polytechnic University, Wuhu 241000, China

Funds:

the National Natural Science Foundation of China 61403001

the National Natural Science Foundation of China 61572032

the Natural Science Foundation of Anhui Province of China 1508085QF136

part by the Natural Science Foundation of Universities of Anhui Province of China KJ2016A058

More Information
    Abstract
  • This paper focuses on the delay-dependent stability for a kind of Markovian jump time-delay systems (MJTDSs), whose transition rates are incompletely known. In order to reduce the computational complexity and achieve better performance, auxiliary function-based double integral inequality is combined with extended Wirtinger's inequality and Jensen inequality to deal with the double integral and the triple integral in augmented Lyapunov-Krasovskii function (ALKF) and their weak infinitesimal generator respectively, the more accurate approximation bounds with a fewer variables are derived. As a result, less conservative stability criteria are proposed in this paper. Finally, numerical examples are given to show the effectiveness and the merits of the proposed method.

     

    • FullText(HTML)
  • loading
    • References(26)
  • [1]
    E. Mazor, A. Averbuch, Y. Bar-Shalom, and J. Dayan, "Interacting multiple model methods in target tracking: a survey, " IEEE Trans. Aerosp. Electron. Syst., vol. 34, no. 1, pp. 103-123, Jan. 1998. http://en.cnki.com.cn/Article_en/CJFDTotal-XTYD200104010.htm
    [2]
    L. X. Zhang and E. K. Boukas, "Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities, " Automatica, vol. 45, no. 2, pp. 463-468, Feb. 2009. http://www.sciencedirect.com/science/article/pii/S0005109808004512
    [3]
    Y. Zhang, Y. He, M. Wu, and J. Zhang, "Stabilization for Markovian jump systems with partial information on transition probability based on free-connection weighting matrices, ", vol. 47, no. 1, pp. 79- 84, Jan. 2011. http://www.sciencedirect.com/science/article/pii/S0005109810003912
    [4]
    Y. Zhang, Y. He, M. Wu, and J. Zhang, "H∞ control for discrete-time Markovian jump systems with partial information on transition probabilities, " Asian J. Control, vol. 15, no. 5, pp. 1397-1406, Sep. 2013.
    [5]
    B. Z. Du, J. Lam, Y. Zou, and Z. Shu, "Stability and stabilization for Markovian jump time-delay systems with partially unknown transition rates, " IEEE Trans. Circuits Syst. I-Reg. Papers, vol. 60, no. 2, pp. 341- 351, Feb. 2013. https://www.researchgate.net/publication/260666045_Stability_and_Stabilization_for_Markovian_Jump_Time-Delay_Systems_With_Partially_Unknown_Transition_Rates
    [6]
    J. Cheng, H. Zhu, S. M. Zhong, Y. P. Zhang, and Y. Y. Li, "Finite-time H∞ control for a class of discrete-time Markovian jump systems with partly unknown time-varying transition probabilities subject to average dwell time switching, " Int. J. Syst. Sci., vol. 46, no. 6, pp. 1080-1093, Apr. 2015.
    [7]
    J. J. Zhao, J. Wang, J. H. Park, and H. Shen, "Memory feedback controller design for stochastic Markov jump distributed delay systems with input saturation and partially known transition rates, " Nonlin. Anal.: Hybrid Syst., vol. 15, pp. 52-62, Feb. 2015. https://www.researchgate.net/publication/264498937_Memory_feedback_controller_design_for_stochastic_Markov_jump_distributed_delay_systems_with_input_saturation_and_partially_known_transition_rates
    [8]
    M. Q. Shen and G. H. Yang, "$H_2$ state feedback controller design for continuous Markov jump linear systems with partly known information, " Int. J. Syst. Sci., vol. 43, no. 4, pp. 786-796, Jan. 2012.
    [9]
    J. Y. Wang, H. G. Zhang, Z. S. Wang, and H. J. Liang, "Stochastic synchronization for Markovian coupled neural networks with partial information on transition probabilities, " vol. 149, pp. 983- 992, Feb. 2015. https://www.researchgate.net/publication/277383097_Stochastic_synchronization_for_Markovian_coupled_neural_networks_with_partial_information_on_transition_probabilities
    [10]
    K. Q. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-Delay Systems. Boston: Birkhäuser, 2003. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1102755
    [11]
    Y. He, Q. G. Wang, C. Lin, and M. Wu, "Delay-range-dependent stability for systems with time-varying delay, " vol. 43, no. 2, pp. 371 -376, Feb. 2007. http://www.sciencedirect.com/science/article/pii/S0005109806003694
    [12]
    P. G. Park, J. W. Ko, and C. K. Jeong, "Reciprocally convex approach to stability of systems with time-varying delays, " vol. 47, no. 1, pp. 235-238, Jan. 2011. https://www.sciencedirect.com/science/article/pii/S0005109810004280
    [13]
    A. Seuret and F. Gouaisbaut, "Wirtinger-based integral inequality: application to time-delay systems, " vol. 49, no. 9, pp. 2860- 2866, Sep. 2013.
    [14]
    A. Seuret and F. Gouaisbaut, "Complete quadratic Lyapunov functionals using Bessel-Legendre inequality, " in Proc. European Control Conf., Strasbourg, France, 2014, pp. 448-453. http://d.old.wanfangdata.com.cn/NSTLHY/NSTL_HYCC0214265154/
    [15]
    J. Sun, G. P. Liu, J. Chen, and D. Rees. "Improved stability criteria for linear systems with time-varying delay, " IET Control Theor. Appl., vol. 4, no. 4, pp. 683-689, Apr. 2010.
    [16]
    Y. Chen and G. Chen, "Stability analysis of systems with time-varying delay via a novel lyapunov functional, " IEEE/CAA J. Autom. Sinica, vol. 6, no 4, pp. 1068-1073, Jul, 2019. http://d.old.wanfangdata.com.cn/Periodical/zdhxb-ywb201904019
    [17]
    Z. C. Li, Y. Bai, and T. Q. Li, "Improved stability and stabilization design for networked control systems using new quadruple-integral functionals, " ISA Trans., vol. 63, pp. 170-181, Jul. 2016. http://www.sciencedirect.com/science/article/pii/S0019057816300453
    [18]
    C. K. Zhang, Y. He, L. Jiang, and M. Wu, "Stability analysis for delayed neural networks considering both conservativeness and complexity, " IEEE Trans. Neural Netw. Learn. Syst., vol. 27, no. 7, pp. 1486-1501, Jul. 2016. http://www.ncbi.nlm.nih.gov/pubmed/26208366
    [19]
    C. K. Zhang, Y. He, L. Jiang, M. Wu, and H. B. Zeng, "Stability analysis of systems with time-varying delay via relaxed integral inequalities, " Syst. Control Lett., vol. 92, pp. 52-61, Jun. 2016.
    [20]
    P. G. Park, W. Lee, and S. Y. Lee, "Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems, " J. Franklin Inst., vol. 352, no. 4, pp. 1378-1396, Apr. 2015. https://www.sciencedirect.com/science/article/abs/pii/S0016003215000198
    [21]
    M. Wu, Y. He, and J. H. She, Stability, Germany Analysis and Robust Control of Time-Delay Systems. Berlin Heidelberg, Germany: Springer-Verlag, 2010. doi: 10.1007/978-3-642-03037-6_5
    [22]
    X. R. Mao, Stochastic Differential Equations and Applications (2nd Edition). Chichester: Horwood Publishing Limited, 2007.
    [23]
    H. J. Kushner, Stochastic Stability and Control. New York: Academic Press, 1967.
    [24]
    Y. Zhang, Y. He, M. Wu, and J. Zhang, "State estimation for Markovian jump systems with time-varying delay and partial information on transition probabilities, " IET Control Theor. Appl., vol. 6, no. 16, pp. 2549- 2555, Nov. 2012.
    [25]
    X. M. Zhang and Q. L. Han, "Event-based H∞ filtering for sampled-data systems, " vol. 51, pp. 55-69, Jan. 2015.
    [26]
    X. D. Zhao and Q. S. Zeng, "Delay-dependent stability analysis for Markovian jump systems with interval time-varying-delays, " Int. J. Automat. Comput., vol. 7, no. 2, pp. 224-229, May 2010. doi: 10.1007/s11633-010-0224-2
    • Related Articles
    • Supplements(0)

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(3)  / Tables(4)

    Get Citation
    PDF
    XML

    Article Metrics

    Article views (1032) PDF downloads(44) Cited by()

    Highlights

    • Inspired by auxiliary function-based double integral inequality, an augmented Lyapunov-Krasovskii function (ALKF) including augmented term and triple integral term is constructed in this paper to investigate the stability of MJTDSs.
    • Compared with Pi satisfying the condition Pi > 0, the constraint condition to guarantee the positiveness of ALKF is weakened by using auxiliary function-based double integral inequality, extended Wirtinger’s inequality and Jensen inequality to estimate the lower bound of the ALKF.
    • The above three inequalities are used to estimate the upper bound of weak infinitesimal generator of the ALKF, as a result, the more accurate approximation bounds with a fewer variables are derived.
    • Consequently, the new criterion on delay-dependent stability for MJTDSs is obtained in this paper. Compared with previous criteria, our results require fewer scalar variables and have less conservative.

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return