Advanced Search
Article Contents
Article Contents

$ \mathcal{H}_{\infty} $ control for fuzzy markovian jump systems based on sampled-data control method

  • * Corresponding author: Jianwei Xia

    * Corresponding author: Jianwei Xia 
The first author is supported by the National Natural Science Foundation of China under Grants 61573177, 61773191, 61973148
Abstract Full Text(HTML) Figure(0) / Table(2) Related Papers Cited by
  • This paper investigates the problems of $ \mathcal{H}_{\infty} $ performance analysis and sampled-data control about fuzzy Markovian jump systems. Firstly, in order to make full use of the information of both intervals $ x(t_{k}) $ to $ x(t) $ and $ x(t) $ to $ x(t_{k+1}) $, we construct the mode-dependent Lyapunov function, which consists of a two-sided closed-loop function. Built on the above Lyapunov function, the stochastically stable conditions with less conservative are given by using linear matrices inequalities (LMIs). Then, a state feedback controller is presented for the studied systems. At last, an example is offered to illustrate the efficiency of our main results.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


    \begin{equation} \\ \end{equation}
  • 加载中
  • Table 1.  $ \gamma_{max} $ for $ h_{min} = 0 $ and different $ h_{max} $

    $ h_{max} $ 0.05 0.15 0.25 0.35
    $ \gamma $ $ 1.7320 $ 1.7678 1.8246 1.9285
     | Show Table
    DownLoad: CSV

    Table 2.  $ \gamma_{max} $ for $ h_{max} = h_{min} $

    $ h $ 0.05 0.15 0.25 0.35
    $ \gamma $ $ 1.7299 $ 1.7576 1.7982 1.8659
     | Show Table
    DownLoad: CSV
  • [1] X. Chang and G. Yang, Nonfragile $H_{\infty}$ filtering of continuous-time fuzzy systems, IEEE Transactions on Signal Processing, 59 (2011), 1528-1538.  doi: 10.1109/TSP.2010.2103068.
    [2] X. Chang, Robust nonfragile $H_{\infty}$ filtering of fuzzy systems with linear fractional parametric uncertainties, IEEE Transactions on Fuzzy Systems, 20 (2012), 1001-1011. 
    [3] G. L. ChenJ. Sun and J. Chen, Mean square exponential stabilization of sampled-data Markovian jump systems, Int J Robust Nonlinear Control, 28 (2018), 5876-5894.  doi: 10.1002/rnc.4351.
    [4] G. ChenJ. Xia and G. Zhuang, Delay-dependent stability and dissipativity analysis of generalized neural networks with Markovian jump parameters and two delay components, J. Frankl. Inst, 353 (2016), 2137-2158.  doi: 10.1016/j.jfranklin.2016.02.020.
    [5] L. S. HuP. Shi and P. M. Frank, Robust sampled-data control for Markovian jump linear systems, Automatica, 42 (2006), 2025-2030.  doi: 10.1016/j.automatica.2006.05.029.
    [6] J. LengH. ZhangD. YanQ. LiuX. Chen and D. Zhang, Digital twin-driven manufacturing cyber-physical system for parallel controlling of smart workshop, Journal of Ambient Intelligence and Humanized Computing, 10 (2019), 1155-1166.  doi: 10.1007/s12652-018-0881-5.
    [7] X. LiX. Yang and T. Huang, Persistence of delayed cooperative models: Impulsive control method, Applied Mathematics and Computation, 342 (2019), 130-146.  doi: 10.1016/j.amc.2018.09.003.
    [8] X. LiJ. Shen and R. Rakkiyappan, Persistent impulsive effects on stability of functional differential equations with finite or infinite delay, Applied Mathematics and Computation, 329 (2018), 14-22.  doi: 10.1016/j.amc.2018.01.036.
    [9] X. Li and M. Bohner, An impulsive delay differential inequality and applications, Computers and Mathematics with Applications, 64 (2012), 1875-1881.  doi: 10.1016/j.camwa.2012.03.013.
    [10] X. LiangJ. XiaG. ChenH. Zhang and Z. Wang, Dissipativity-based sampled-data control for fuzzy Markovian jump systems, Applied Mathematics and Computation, 361 (2019), 552-564.  doi: 10.1016/j.amc.2019.05.038.
    [11] F. LiP. ShiC. Lim and L. Wu, Fault detection filtering for nonhomogeneous markovian jump systems via a fuzzy approach, IEEE Transactions on Fuzzy Systems, 26 (2018), 131-141.  doi: 10.1109/TFUZZ.2016.2641022.
    [12] C. Lin, G. Wang, T. Lee and Y. He, LMI Approach to Analysis and Control of Takagi-Sugeno Fuzzy Systems With Time Delay, Lecture Notes in Control and Information Sciences, 351. Springer, Berlin, 2007.
    [13] X. LiangJ. XiaG. ChenH. Zhang and Z. Wang, Dissipativity-based non-fragile sampled-data control for fuzzy Markovian jump systems, Int. J. Fuzzy Syst., 21 (2019), 1709-1723.  doi: 10.1007/s40815-019-00691-1.
    [14] J. H. Park, H. Shen, X. H. Chang and T. H. Lee, Recent Advances in Control and Filtering of Dynamic Systems with Constrained Signals, Cham, Switzerland: Springer, 2019. doi: 10.1007/978-3-319-96202-3.
    [15] J. H. Park, T. H. Lee, Y. Liu and J. Chen, Dynamic Systems with Time Delays: Stability and Control, Singapore, Springer-Nature, 2019. doi: 10.1007/978-981-13-9254-2.
    [16] H. ShenJ. H. ParkL. Zhang and Z. G. Wu, Robust extended dissipative control for sampled-data Markov jump systems, Int J Control, 87 (2014), 1549-1564.  doi: 10.1080/00207179.2013.878478.
    [17] P. ShiF. LiL. Wu and C. C. Lim, $h_{\infty}$ Neural network-based passive filtering for delayed neutral-type semi-Markovian jump systems, IEEE Trans Neural Netw Learn Syst, 28 (2017), 2101-2114. 
    [18] X. Song, Z. Wang and H. Shen, et al, A unified method to energy-to-peak filter design for networked Markov switched singular systems over a finite-time interval, Journal of the Franklin Institute, 354 (2017), 7899–7916. doi: 10.1016/j.jfranklin.2017.09.018.
    [19] X. Song, M. Wang and S. Song, et al, Reliable state estimation for Markovian jump reactiondiffusion neural networks with sensor saturation and asynchronous failure, IEEE Access, 6 (2018), 50066–50076. doi: 10.1109/ACCESS.2018.2868060.
    [20] X. SongS. Song and Bo Li, Adaptive projective synchronization for time-delayed fractional-order neural networks with uncertain parameters and its application in secure communications, Transactions of the Institute of Measurement and Control, 40 (2018), 3078-3087.  doi: 10.1177/0142331217714523.
    [21] S. Song and X. Song, Multi-switching adaptive synchronization of two fractional-order chaotic systems with different structure and different order, International Journal of Control, Automation and Systems, 15 (2017), 1524-1535.  doi: 10.1007/s12555-016-0097-4.
    [22] W. SunJ. XiaG. ZhuangX. Huang and H. Shen, Adaptive fuzzy asymptotically tracking control of full state constrained nonlinear system based on a novel Nussbaum-type function, Journal of the Franklin Institute, 356 (2019), 1810-1827.  doi: 10.1016/j.jfranklin.2018.11.023.
    [23] W. Sun, S. Su, Y. Wu, J. Xia and V. Nguyen, Adaptive fuzzy control with high-order barrier Lyapunov functions for high-order uncertain nonlinear systems with full-state constraints, IEEE Transactions on Cybernetics, 2019, 1–9. doi: 10.1109/TCYB.2018.2890256.
    [24] W. SunS. SuJ. Xia and V. Nguyen, Adaptive fuzzy tracking control of flexible-joint robots with full-state constraints, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 49 (2019), 2201-2209.  doi: 10.1109/TSMC.2018.2870642.
    [25] W. Sun, S. Su, G. Dong and W. Bai, Reduced adaptive fuzzy tracking control for high-order stochastic nonstrict feedback nonlinear system with full-state constraints, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 1–11. doi: 10.1109/TSMC.2019.2898204.
    [26] W. Sun, S. Su, J. Xia and Y. Wu, Adaptive tracking control of wheeled inverted pendulums with periodic disturbances, IEEE Transactions on Cybernetics, 50 (2020), 1867–1876. doi: 10.1109/TCYB.2018.2884707.
    [27] H. ShenZ. WangX. Huang and J. Wang, Fuzzy dissipative control for nonlinear Markovian jump systems via retarded feedback, J. Frankl.Inst, 351 (2014), 3797-3817.  doi: 10.1016/j.jfranklin.2013.02.031.
    [28] H. ShenY. Z. MenZ. G. Wu and J. H. Park, Nonfragile $\mathcal{H}_{\infty}$ control for fuzzy Markovian jump systems under fast sampling singular perturbation, IEEE Transactions on Fuzzy Systems, 48 (2018), 2058-2069. 
    [29] H. ShenF. LiH. YanH. Karimi and H. Lam, Finite-time event-triggered $\mathcal{H}_{\infty}$ control for T-S fuzzy Markov jump systems, IEEE Transactions on Fuzzy Systems, 26 (2018), 3122-3135. 
    [30] J. WangH. WuL. Guo and Y. Luo, Robust $H_{\infty}$ fuzzy control for uncertain nonlinear Markovian jump systems with time-varying delay, Fuzzy Sets and Systems, 212 (2013), 41-61.  doi: 10.1016/j.fss.2012.07.010.
    [31] Z. G. WuP. ShiH. Su and J. Chu, Asynchronous $l_{2}-l_{\infty}$ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities, Automatica, 50 (2014), 180-186.  doi: 10.1016/j.automatica.2013.09.041.
    [32] Z. WuP. ShiH. Su and R. Lu, Dissipativity-based sampled-data fuzzy control design and its application to truck-trailer system, IEEE Transactions on Fuzzy Systems, 23 (2015), 1669-1679.  doi: 10.1109/TFUZZ.2014.2374192.
    [33] J. XiaG. Chen and W. Sun, Extended dissipative analysis of generalized Markovian switching neural networks with two delay components, Neurocomputing, 260 (2017), 275-283.  doi: 10.1016/j.neucom.2017.05.005.
    [34] J. Xia, J. Zhang, J. Feng, Z. Wang and G. Zhuang, Command filter-based adaptive fuzzy control for nonlinear systems with unknown control directions, IEEE Transactions on Systems, Man and Cybernetics: Systems, In Press.
    [35] J. XiaJ. ZhangW. SunB. Y. Zhang and Z. Wang, Finite-time adaptive fuzzy control for nonlinear systems with full state constraints, IEEE Transactions on Systems, Man and Cybernetics: Systems, 49 (2019), 1541-1548.  doi: 10.1109/TSMC.2018.2854770.
    [36] S. Y. XuJ. Lam and X. R. Mao, Delay-dependent $H_{\infty}$ control and filtering for uncertain markovian jump systems with time-varying delays, IEEE Transactions on Circuits and Systems, 54 (2007), 2070-2077.  doi: 10.1109/TCSI.2007.904640.
    [37] D. YangX. Li and J. Qiu, Output tracking control of delayed switched systems via state-dependent switching and dynamic output feedback, Nonlinear Analysis: Hybrid Systems, 32 (2019), 294-305.  doi: 10.1016/j.nahs.2019.01.006.
    [38] X. YangX. LiQ. Xi and P. Duan, Review of stability and stabilization for impulsive delayed systems, Mathematical Biosciences and Engineering, 15 (2018), 1495-1515.  doi: 10.3934/mbe.2018069.
    [39] H. ZengK. TeoY. HeH. Xu and W. Wang, Sampled-data synchronization control for chaotic neural networks subject to actuator saturation, Neurocomputing, 260 (2017), 25-31.  doi: 10.1016/j.neucom.2017.02.063.
    [40] H. ZengY. HeM. Wu and J. She, Free-matrix-based integral inequality for stability analysis of systems with time-varying delay, IEEE Trans. Automat. Contr, 60 (2015), 2768-2772.  doi: 10.1109/TAC.2015.2404271.
    [41] H. ZengK. Teo and Y. He, A new looped-functional for stability analysis of sampled-data systems, Automatica, 82 (2017), 328-331.  doi: 10.1016/j.automatica.2017.04.051.
    [42] H. ZengK. TeoY. He and W. Wang, Sampled-data-based dissipative control of T-S fuzzy systems, Applied Mathematical Modelling, 65 (2019), 415-427.  doi: 10.1016/j.apm.2018.08.012.
    [43] G. ZhuangJ. XiaW. SunQ. MaZ. Wang and Y. Wang, Normalization and stabilization of neutral descriptor hybrid systems based on P-D feedback control, Journal of the Franklin Institute, 357 (2020), 1070-1089.  doi: 10.1016/j.jfranklin.2019.10.020.
    [44] B. ZhangW. X. Zheng and S. Xu, $h_{\infty}$ Filtering of Markovian jump delay systems based on a new performance index, IEEE Trans Circuits Syst I Reg Pap, 60 (2013), 1250-1263.  doi: 10.1109/TCSI.2013.2246213.
    [45] J. ZhangJ. XiaW. SunG. Zhuang and Z. Wang, Finite-time tracking control for stochastic nonlinear systems with full state constraints, Applied Mathematics and Computation, 338 (2018), 207-220.  doi: 10.1016/j.amc.2018.05.040.
    [46] J. ZhangX. Liang and J. Xia, Adaptive tracking control for stochastic nonlinear systems with full state constraints, Journal of Liaocheng University (Natural Science Edition), 32 (2019), 8-13. 
    [47] G. ZhuangS. XuJ. XiaQ. Ma and Z. Zhang, Non-fragile delay feedback control for neutral stochastic Markovian jump systems with time-varying delays, Applied Mathematics and Computation, 355 (2019), 21-32.  doi: 10.1016/j.amc.2019.02.057.
    [48] G. ZhuangQ. MaB. ZhangS. Xu and J. Xia, Admissibility and stabilization of stochastic singular Markovian jump systems with time delays, Systems and Control Letters, 114 (2018), 1-10.  doi: 10.1016/j.sysconle.2018.02.004.
    [49] G. ZhuangS. XuB. ZhangH. Xu and Y. Chu, Robust $H_{\infty}$ deconvolution filtering for uncertain singular Markovian jump systems with time-varying delays, International Journal of Robust and Nonlinear Control, 26 (2016), 2564-2585.  doi: 10.1002/rnc.3461.
    [50] G. ZhuangS. XuJ. XiaQ. Ma and Z. Zhang, Non-fragile delay feedback control for neutra stochastic Markovian jump systems with time-varying delays, Applied Mathematics and Computation, 355 (2019), 21-32.  doi: 10.1016/j.amc.2019.02.057.
    [51] G. ZhuangJ. XiaJ. FengW. Sun and B. Zhang, Admissibilization for implicit jump systems with mixed retarded delays based on reciprocally convex integral inequality and Barbalat's lemma, IEEE Trans. Syst., Man, Cybern., 16 (2020), 1-11.  doi: 10.1109/TSMC.2020.2964057.
  • 加载中



Article Metrics

HTML views(493) PDF downloads(298) Cited by(0)

Access History



    DownLoad:  Full-Size Img  PowerPoint