### Mean-Square Stabilization of Networked Sampled-Data Systems with Packet Losses: Critical Sampling Intervals

WANG Chao, WANG Bingchang

1. School of Control Science and Engineering, Shandong University, Jinan 250061, China
• Received:2020-08-09 Revised:2021-06-30 Online:2022-08-25 Published:2022-08-02
• Contact: WANG Bingchang,Email:bcwang@sdu.edu.cn
• Supported by:
This research was supported by the National Natural Science Foundation of China under Grant Nos. 61773241, 62122043 and the Youth Innovation Group Project of Shandong University under Grant No. 2020QNQT016.

WANG Chao, WANG Bingchang. Mean-Square Stabilization of Networked Sampled-Data Systems with Packet Losses: Critical Sampling Intervals[J]. Journal of Systems Science and Complexity, 2022, 35(4): 1278-1292.

This paper studies the stabilizing problem of networked sampled-data linear systems with independent and identically distribution (i.i.d.) packet dropouts. First of all, for the sampled-data system without packet losses, the necessary and sufficient conditions for the critical sampling intervals are given to ensure the mean square stability where zero order holder and generalized holder are adopted, respectively. Secondly, for the sampled-data system with i.i.d. packet losses, necessary and sufficient conditions for the critical sampling intervals are given to ensure the mean square stability where the zero order holder control is adopted. The random sampling framework is used to examine the case that the value of the control signal is not zero when the packet loss occurs, but the value of the previous control signal when the data packet is not lost. For the sampled-data system with i.i.d. packet losses, the range of the sampling interval is given to ensure the mean square stability where the generalized holder control is adopted. Some numerical simulations are provided to validate the theoretical results.
 [1] Chen T and Francis B, Optimal Sampled-Data Control Systems, Springer, London, 1995.[2] Åström K J and Wittenmark B, Computer-Controlled Systems-Theory and Design, Prentice Hall, New Jersey, 1997.[3] Ohno K, Hirata M, and Horowitz R, A comparative study of the use of the generalized hold function for HDDs, IEEE/ASME Trans. on Mechatronics, 2005, 10(1): 26-33.[4] Meng X, Wang B C, Chen T, et al., Sensing and actuation strategies for event triggered stochastic optimal control, Proceedings of the 52nd IEEE Conference on Decision and Control, Florence, 2013.[5] Hespanha M, Naghshtabrizi P, and Xu Y, A survey of recent results in networked control systems, Proceedings of the IEEE, 2007, 95(1): 138-162.[6] Hadjicostis C and Touri R, Feedback control utilizing packet dropping network links, Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, 2002.[7] Wu J and Chen T, Design of networked control systems with packet dropouts, IEEE Trans. on Automatic Control, 2007, 52(7): 1314-1319.[8] Dong Y, Han Q, and Chen P, State feedback controller design of networked control systems, Proceedings of IEEE International Conference on Control Applications, Taipei, 2004.[9] Yu M, Wang L, Xie G, et al., Stabilization of networked control systems with data packet dropout via switched system approach, Proceedings of IEEE International Symposium on Computer Aided Control Systems Design, Taipe, 2004.[10] Xie L and Xie L, Stabilizing sampled-data linear systems with Markovian packet losses and random sampling, IFAC Proceedings Volumes, 2008, 41(2): 599-604.[11] Montestruque L and Antsaklis P, Stability of model-based networked control systems with timevarying transmission times, IEEE Trans. on Automatic control, 2004, 49(9): 1562-1572.[12] Xie L and Xie L, Stability analysis of networked sampled-data linear systems with Markovian packet losses, IEEE Trans. on Automatic Control, 2009, 54(6): 1368-1374.[13] Wu J, Meng Z, Yang T, et al., Critical sampling rate for sampled-data consensus over random networks. Proceedings of the 54th IEEE Conference on Decision and Control, Osaka, 2015.[14] Wu J, Meng Z, Yang T, et al., Sampled-data consensus over random networks, IEEE Trans. on Signal Processing, 2016, 64(17): 4479-4492.[15] Montestruque L and Antsaklis P, On the model-based control of networked systems, Automatica, 2003, 39(10): 1837-1843.[16] Kabamba P and Yang C, Simultaneous controller design for linear time-invariant systems, IEEE Trans. on Automatic Control, 1991, 36(1): 106-111.[17] Kabamba P, Control of linear systems using generalized sampled-data hold functions, IEEE Trans. on Automatic Control, 1987, 32(9): 772-783.[18] You K and Xie L, Minimum data rate for mean square stabilization of discrete LTI systems over lossy channels, IEEE Trans. on Automatic Control, 2010, 55(10): 2373-2378.[19] Qi Q and Zhang H, Output feedback control and stabilization for networked control systems with packet losses, IEEE Trans. on Cybernetics, 2017, 47(8): 2223-2234.[20] Sun H, Chen J, and Sun J, Observer-based output feedback control for sampled-data system with Markovian packet losses and stochastic sampling, Proceedings of IECON 2017— 43rd Annual Conference of the IEEE Industrial Electronics Society, 2017.[21] Yang H, Xu Y, and Zhang J, Event-driven control for networked control systems with quantization and Markov packet losses, IEEE Trans. on Cybernetics, 2017, 47(8): 2235-2243.
 No related articles found!
Viewed
Full text

Abstract