GNSS World of China

Volume 45 Issue 5
Oct.  2020
Turn off MathJax
Article Contents
Article Navigation >  GNSS World of China  > 2020  >  45(5): 77-83
WANG Qing, ZHANG Yi. Sampled-data control of Markov jump system via a fragmentation functional[J]. GNSS World of China, 2020, 45(5): 77-83. doi: 10.13442/j.gnss.1008-9268.2020.05.014
Citation: WANG Qing, ZHANG Yi. Sampled-data control of Markov jump system via a fragmentation functional[J]. GNSS World of China, 2020, 45(5): 77-83. doi: 10.13442/j.gnss.1008-9268.2020.05.014
shu

Sampled-data control of Markov jump system via a fragmentation functional

doi: 10.13442/j.gnss.1008-9268.2020.05.014

  • College of Instrument Science and Engineering,Southeast University,Nanjing 210096,China

  • Publish Date: 2021-02-24
    Abstract
  • Markovian jump systems is a most important mixed stochastic system in practice application,the sampled-data control problem of Markov jump system is studied in this paper.According to a continuous Markov jump system model and Lyapunov-Krasovskii stability theorem,the whole sampling interval is divided into four parts by introducing two adjustable parameters.Based on the four sampling intervals,two corresponding expressions of state space are proposed.Novel Lyapunov-Krasovskii functional which can fally use the status information of four frogmentation interual is built.then,using the integral inequality methods to estimate functional derivative,a new sampled-data control Markov jump system stability criterion is obtained.Finally,an example of a nonlinear mass spring damper system and an actual ship positioning system are given.After the establishment of simulation,the maximum sampling interval obtained is much larger than the results of similar literatures,indicating the superiority of the method.

     

    • FullText(HTML)
  • loading
    • References(20)
  • [1]
    LI H,WANG Y Y,YAO D Y,et al.A sliding mode approach to stabilization of nonlinear Markovian jump singularly perturbed systems［J］.Automatica,2018（97）:404-413.DOI: 10.1007／978-3-211-73017-1.
    [2]
    高学泽,魏文军.马尔可夫参数自适应IMM算法在列车定位中的应用［J］.传感器与微系统,2019,38(1):155-157,160.
    [3]
    吴庆祥,DAVID B.可移动机器人的马尔可夫自定位算法研究［J］.自动化学报,2003,29(1):154-160.
    [4]
    唐龙,张小红,吕翠仙,等.精密单点定位估计GPS卫星的P1-C1码偏差及稳定性分析［J］.全球定位系统,2011,36(2):1-5.
    [5]
    罗峰.CORS基准站的稳定性分析与研究［J］.全球定位系统,2014,39(1):42-45,55.
    [6]
    KWON N K,PARK I S,PARK P G.H∞control for singular markovian jump systems with incomplete knowledge of transition probabilities［J］.Applied mathematics and computation,2017（295）:126-135.DOI: 10.1016／j.amc.2016.09.004.
    [7]
    KWON N K,PARK I S,PARK P G,et al.Dynamic output-feedback control for singular markovian jump system:LMI approach［J］.IEEE transactions on automatic control,2017,62(10):5396-5400.DOI: 10.1109／TAC.2017.2691311.
    [8]
    WU Z G,SHI P,SU H,et al.Sampled-data exponential synchronization of complex dynamical networks with time-varying coupling delay［J］.IEEE transactions on neural networks and learning systems,2013,24(8):1177-1187.DOI: 10.1109／TNNLS.2013.2253122.
    [9]
    ZHAO D W,DING F G,ZHOU L,et al.Robust H∞control of neutral system with time-delay for dynamic positioning ships［J］.Mathematical problems in engineering,2015.DOI: 10.1155／2014／976925.
    [10]
    YANG S,ZHENG M.H∞fault-tolerant control for dynamic positioning ships based on sampled-data［J］.Journal of control engineering and applied informatics,2018,20(4):32-39.
    [11]
    ZHENG M J,ZHOU Y J,YANG S H,et al.Robust H∞control of neutral system for sampled-data dynamic positioning ships［J］.IMA journal of mathematical control and information,2019,36(4):1325-1345.DOI: 10.1093／imamci／dny029.
    [12]
    WANG Y Y,XIA Y Q,ZHOU P F.Fuzzy-model-based sampled-data control of chaotic systems:a fuzzy time-dependent lyapunov—krasovskii functional approach［J］.IEEE transactions on fuzzy systems,2017,25(6):1672-1684.DOI: 10.1109／TFUZZ.2016.2617378.
    [13]
    XU S D,SUN G H,LI Z,et al.Finite-time robust fuzzy control for non-linear Markov jump systems under aperiodic sampling and actuator constraints［J］.IET control theory ＆ applications,2017,11(15):2419-2431.DOI: 10.1049／iet-cta.2016.1609.
    [14]
    MA W W,JIA X C,YANG F W,et al.An impulsive-switched-system approach to aperiodic sampled-data systems with time-delay control［J］.International journal of robust and nonlinear control,2018,28(4):2484-2494.DOI: 10.1002／rnc.4030.
    [15]
    SEURET A.A novel stability analysis of linear systems under asynchronous samplings［J］.Automatica,2012, 48(1):177-182.DOI: 10.1016／j.automatica.2011.09.033.
    [16]
    ZENG H B,TEO K L,HE Y.A new looped-functional for stability analysis of sampled-data systems［J］.Automatica,2017（82）:328-331.DOI: 10.1016／j.automatica.2017.04.051.
    [17]
    HU L S,SHI P,FRANK P M.Robust sampled-data control for Markovian jump linear systems［J］.Automatica,2006,42(11):2025-2030.DOI: 10.1016／j.automatica.2006.05.029.
    [18]
    SHEN H,PARK J H,ZHANG L X,et al.Robust extended dissipative control for sampled-data Markov jump systems［J］.International journal of control,2014,87(8):1549-1564.DOI: 10.1080／00207179.2013.878478.
    [19]
    PARK J M,PARK P G.Sampled-data control for continuous-time Markovian jump linear systems via a fragmented-delay state and its state-space model［J］.Journal of the franklin institute,2019,356(10):5073-5086.DOI: 10.1016／j.jfranklin.2019.02.033.
    [20]
    ZHANG X M,HAN Q L,ZENG Z G.Hierarchical type stability criteria for delayed neural networks via canonical Bessel-Legendre inequalities［J］.IEEE transactions on cybernetics,2018,48(5):1660-1671.DOI: 10.1109／TCYB.2017.2776283.
    • Relative Articles
    • Supplements(0)
    • Cited By
  • 加载中

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
    Get Citation
    PDF
    XML

    Article Metrics

    Article views (361) PDF downloads(17) Cited by()
    Proportional views
    Related

    Copyright © 2009《 GNSS World of China 》 Editorial Office

    Address：84 Jianshe Dong Lu, Muye District, Xinxiang City, Henan Province, ChinaChina Pos：453000Tel：0373-3712411Fax：0373-3052232Email：qqdwxt@126.com

    Supported by: Beijing Renhe Information Technology Co. Ltd    

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return