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Volume 7 Issue 5
Sep.  2020

IEEE/CAA Journal of Automatica Sinica

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Yiming Cheng, Xu Zhang, Tianhe Liu and Changhong Wang, "Finite-time Control of Discrete-time Systems With Variable Quantization Density in Networked Channels," IEEE/CAA J. Autom. Sinica, vol. 7, no. 5, pp. 1394-1402, Sept. 2020. doi: 10.1109/JAS.2020.1003087
Citation: Yiming Cheng, Xu Zhang, Tianhe Liu and Changhong Wang, "Finite-time Control of Discrete-time Systems With Variable Quantization Density in Networked Channels," IEEE/CAA J. Autom. Sinica, vol. 7, no. 5, pp. 1394-1402, Sept. 2020. doi: 10.1109/JAS.2020.1003087

Finite-time Control of Discrete-time Systems With Variable Quantization Density in Networked Channels

doi: 10.1109/JAS.2020.1003087
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  • This paper is concerned with the problem of finite-time control for a class of discrete-time networked systems. The measurement output and control input signals are quantized before being transmitted in communication network. The quantization density of the network is assumed to be variable depending on the throughputs of network for the sake of congestion avoidance. The variation of the quantization density modes satisfies persistent dwell-time (PDT) switching which is more general than dwell-time switching in networked channels. By using a quantization-error-dependent Lyapunov function approach, sufficient conditions are given to ensure that the quantized systems are finite-time stable and finite-time bounded with a prescribed ${\cal H}_{\infty }$ performance, upon which a set of controllers depending on the mode of quantization density are designed. In order to show the effectiveness of the designed ${\cal H}_{\infty }$ controller, we apply the developed theoretical results to a numerical example.

     

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  • [1]
    Y.-F. Huang, S. Werner, J. Huang, N. Kashyap, and V. Gupta, “State estimation in electric power grids: Meeting new challenges presented by the requirements of the future grid,” IEEE Signal Processing Magazine, vol. 29, no. 5, pp. 33–43, 2012. doi: 10.1109/MSP.2012.2187037
    [2]
    Z. P. Ning, L. X. Zhang, J. de Juses Rubio, and X. Y. Yin, “Asynchronous filtering for discrete-time fuzzy affine systems with variable quantization density,” IEEE Trans. Cybernetics, vol. 47, no. 1, pp. 153–164, 2017. doi: 10.1109/TCYB.2015.2509170
    [3]
    A. Kahrobaeian and Y. A.-R. I. Mohamed, “Networked-based hybrid distributed power sharing and control for islanded microgrid systems,” IEEE Trans. Power Electronics, vol. 30, no. 2, pp. 603–617, 2014.
    [4]
    M. Yu, L. Wang, T. G. Chu, and G. M. Xie, “Stabilization of networked control systems with data packet dropout and network delays via switching system approach,” in Proc. 43rd IEEE Conf. Decision & Control, 2004. 3539–3544.
    [5]
    X. Y. Yin, Z. J. Li, L. X. Zhang, and M. H. Han, “Distributed state estimation of sensor-network systems subject to markovian channel switching with application to a chemical process,” IEEE Trans. Systems Man &Cybernetics Systems, vol. 48, no. 6, pp. 864–874, 2018.
    [6]
    S. Wang, M. Zeng, H. P. Ju, L. X. Zhang, T. Hayat, and A. Alsaedi, “Finitetime control for networked switched linear systems with an event-driven communication approach,” Int. J. Systems Science, vol. 48, no. 2, pp. 236–246, 2017. doi: 10.1080/00207721.2016.1177130
    [7]
    Y. Z. Zhu, Z. X. Zhong, M. V. Basin, and D. H. Zhou, “A descriptor system approach to stability and stabilization of discrete-time switched pwa systems,” IEEE Trans. Autom. Control, vol. 63, no. 10, pp. 3456–3463, 2018. doi: 10.1109/TAC.2018.2797173
    [8]
    S. Yuan, L. X. Zhang, B. D. Schutter, and S. Baldi, “A novel Lyapunov function for a non-weighted L2 gain of asynchronously switched linear systems,” Automatica, vol. 87, pp. 310–317, 2018. doi: 10.1016/j.automatica.2017.10.018
    [9]
    Y. Z. Zhu and W. X. Zheng,“Multiple lyapunov functions analysis approach for discrete-time switched piecewise-affine systems under dwelltime constraints,” IEEE Trans. Autom. Control, 2019.
    [10]
    H. J. Gao and T. W. Chen, “A new approach to quantized feedback control systems,” Automatica, vol. 44, no. 2, pp. 534–542, 2008. doi: 10.1016/j.automatica.2007.06.015
    [11]
    Y. Z. Zhu, W. X. Zheng, and D. H. Zhou, “Quasi-synchronization of discretetime lure-type switched systems with parameter mismatches and relaxed pdt constraints,” IEEE Trans. Cybernetics, vol. 50, no. 5, pp. 2026–2037, 2020. doi: 10.1109/TCYB.2019.2930945
    [12]
    L. X. Zhang, Z. P. Ning, and W. X. Zheng, “Observer-based control for piecewise-affine systems with both input and output quantization,” IEEE Trans. Autom. Control, vol. 62, no. 11, pp. 5858–5865, 2017. doi: 10.1109/TAC.2016.2641585
    [13]
    Z. P. Ning, L. X. Zhang, J. T. Liang, and J. de. J. Rubio, “State estimation for T-S fuzzy affine systems with variable quantization density,” in Proc. 6th Int. Conf. Intelligent Control & Information Processing, 2016, pp. 274–279.
    [14]
    Z. P. Ning, L. X. Zhang, J. de. J. Rubio, and X. Y. Yin, “Asynchronous filtering for discrete-time fuzzy affine systems with variable quantization density,” IEEE Trans. Cybernetics, vol. 47, no. 1, pp. 153–164, 2016.
    [15]
    G. V. Kamenkov, “On stability of motion over a finite interval of time,” Akad. Nauk SSSR. Prikl. Mat. Meh, pp. 529–540, 1953.
    [16]
    K. K. Gupta and S. Jain, “A novel multilevel inverter based on switched dc sources,” IEEE Trans. Industrial Electronics, vol. 61, no. 7, pp. 3269–3278, 2014. doi: 10.1109/TIE.2013.2282606
    [17]
    K. C. Walker, Y. J. Pan, and J. Gu, “Bilateral teleoperation over networks based on stochastic switching approach,” IEEE/ASME Trans. Mechatronics, vol. 14, no. 5, pp. 539–554, 2009. doi: 10.1109/TMECH.2009.2007126
    [18]
    P. C. Pellanda, P. Apkarian, H. D. Tuan, and D. Alazard, “Missile autopilot design via a multi-channel lft/lpv control method,” IFAC Proceedings Volumes, vol. 35, no. 1, pp. 107–112, 2002.
    [19]
    F. Amato, G. D. Tommasi, and A. Pironti, “Necessary and sufficient conditions for finite-time stability of impulsive dynamical linear systems,” Automatica, vol. 49, no. 8, pp. 2546–2550, 2013. doi: 10.1016/j.automatica.2013.04.004
    [20]
    M. N. Elbsat and E. E. Yaz, “Robust and resilient finite-time bounded control of discrete-time uncertain nonlinear systems,” Automatica, vol. 49, no. 7, pp. 2292–2296, 2013. doi: 10.1016/j.automatica.2013.04.003
    [21]
    J. Song, Y. G. Niu, and Y. Y. Zou, “Robust finite-time bounded control for discrete-time stochastic systems with communication constraint,” IET Control Theory &Applications, vol. 9, no. 13, pp. 2015–2021, 2015.
    [22]
    S. Shi, Z. P. Shi, Z. Y. Fei, and Z. Liu, “Finite-time output feedback control for discrete-time switched linear systems with mode-dependent persistent dwell-time,” J. Franklin Institute, vol. 355, no. 13, pp. 5560–5575, 2018. doi: 10.1016/j.jfranklin.2018.05.057
    [23]
    L. X. Zhang, S. L. Zhuang, P. Shi, and Y. Z. Zhu, “Uniform tube based stabilization of switched linear systems with mode-dependent persistent dwell-time,” IEEE Trans. Autom. Control, vol. 60, no. 11, pp. 2994–2999, 2015. doi: 10.1109/TAC.2015.2414813
    [24]
    X. Z. Lin, H. B. Du, S. H. Li, and Y. Zou, “Finite-time stability and finitetime weighted L2-gain analysis for switched systems with time-varying delay,” IET Control Theory &Applications, vol. 7, no. 7, pp. 1058–1069, 2013.

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    Highlights

    • the interested quantization density of networked system is modeled as a class of switched systems with persistent dwell time switching signals.
    • a class of Lyapunov-like functions that are both mode-dependent and quantization density-dependent is developed.
    • the switched system with PDT switching is finite-time bounded and has a prescribed H∞ performance.

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