Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2013, Special Issue (2013), Article ID 715072, 10 pages.

Stability Analysis of Networked Control Systems with Random Time Delays and Packet Dropouts Modeled by Markov Chains

Li Qiu, Fengqi Yao, and Xiaopin Zhong

Full-text: Open access

Abstract

This paper investigates the stability analysis problem for a class of discrete-time networked control systems (NCSs) with random time delays and packet dropouts based on unified Markov jump model. The random time delays and packet dropouts existed in feedback communication link are modeled by two independent Markov chains; the resulting closed-loop system is described by a new Markovian jump linear system (MJLS) with Markov delays. Sufficient conditions of the stochastic stability for NCSs is obtained by constructing a novel Lyapunov functional, and the mode-dependent output feedback controller design method is presented based on linear matrix inequality (LMI) technique. A numerical example is given to illustrate the effectiveness of the proposed method.

Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 715072, 10 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394806126

Digital Object Identifier
doi:10.1155/2013/715072

Mathematical Reviews number (MathSciNet)
MR3103041

Zentralblatt MATH identifier
06950836

Citation

Qiu, Li; Yao, Fengqi; Zhong, Xiaopin. Stability Analysis of Networked Control Systems with Random Time Delays and Packet Dropouts Modeled by Markov Chains. J. Appl. Math. 2013, Special Issue (2013), Article ID 715072, 10 pages. doi:10.1155/2013/715072. https://projecteuclid.org/euclid.jam/1394806126


Export citation

References

  • J. P. Hespanha, P. Naghshtabrizi, and Y. Xu, “A survey of recent results in networked control systems,” Proceedings of the IEEE, vol. 95, no. 1, pp. 138–172, 2007.
  • M. C. F. Donkers, W. P. M. H. Heemels, N. van de Wouw, and L. Hetel, “Stability analysis of networked control systems using a switched linear systems approach,” IEEE Transactions on Automatic Control, vol. 56, no. 9, pp. 2101–2115, 2011.
  • L. X. Zhang, H. J. Gao, and O. Kaynak, “Network-induced constraints in networked control systems–-a survey,” IEEE Transactions on Automatic Control, vol. 9, no. 1, pp. 403–416, 2013.
  • J. Xiong and J. Lam, “Stabilization of linear systems over networks with bounded packet loss,” Automatica, vol. 43, no. 1, pp. 80–87, 2007.
  • Z. Wang, F. Yang, D. W. C. Ho, and X. Liu, “Robust ${H}_{\infty }$ control for networked systems with random packet losses,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 37, no. 4, pp. 916–924, 2007.
  • W.-A. Zhang and L. Yu, “Output feedback stabilization of networked control systems with packet dropouts,” IEEE Transactions on Automatic Control, vol. 52, no. 9, pp. 1705–1710, 2007.
  • T. Jia, Y. Niu, and X. Wang, “${H}_{\infty }$ control for networked systems with data packet dropout,” International Journal of Control, Automation and Systems, vol. 8, no. 2, pp. 198–203, 2010.
  • J. Wu and T. Chen, “Design of networked control systems with packet dropouts,” IEEE Transactions on Automatic Control, vol. 52, no. 7, pp. 1314–1319, 2007.
  • B. Xue, S. Li, and Q. Zhu, “Moving horizon state estimation for networked control system with multiple packet dropouts,” IEEE Transactions on Automatic Control, vol. 57, no. 9, pp. 2360–2366, 2012.
  • Q. Lu, L. Zhang, M. Basin, and H. Tian, “Analysis and synthesis for networked control systems with uncertain rate of packet losses,” Journal of the Franklin Institute, vol. 349, no. 7, pp. 2500–2514, 2012.
  • B. Ding, “Stabilization of linear systems over networks with bounded packet loss and its use in model predictive control,” Automatica, vol. 47, no. 11, pp. 2526–2533, 2011.
  • D. E. Quevedo and D. Nešić, “Robust stability of packetized predictive control of nonlinear systems with disturbances and Markovian packet losses,” Automatica, vol. 48, no. 8, pp. 1803–1811, 2012.
  • B. Ding and L. Xie, “Stabilization of linear systems over networks with double-sided, finite bounded, arbitrary packet loss,” in Proceedings of the IEEE International Conference on Control and Automation (ICCA '09), pp. 920–925, December 2009.
  • E. Tian and D. Yue, “A new state feedback ${H}_{\infty }$ control of networked control systems with time-varying network conditions,” Journal of the Franklin Institute, vol. 349, no. 3, pp. 891–914, 2012.
  • D. Yue, E. Tian, and Q.-L. Han, “A delay system method for designing event-triggered controllers of networked control systems,” IEEE Transactions on Automatic Control, vol. 58, no. 2, pp. 475–481, 2013.
  • M. Azadegan, M. T. H. Beheshti, and B. Tavassoli, “Robust output feedback control of networked control systems with random delay modeled by Markov chain,” in Proceedings of the 20th Iranian Conference on Electrical Engineering, pp. 587–592, Tehran, Iran, 2012.
  • J. Nilsson, Real-Time Control Systems with Delays, Lund Institute of Technology, Lund, Sweden, 1998.
  • L. Xiao, A. Hassibi, and J. P. How, “Control with random communication delays via a discrete-time jump system approach,” in Proceedings of the 2000 American Control Conference, pp. 3545–3550, June 2000.
  • Y. Shi and B. Yu, “Output feedback stabilization of networked control systems with random delays modeled by Markov chains,” IEEE Transactions on Automatic Control, vol. 54, no. 7, pp. 1668–1674, 2009.
  • M. B. G. Cloosterman, N. van de Wouw, W. P. M. H. Heemels, and H. Nijmeijer, “Stability of networked control systems with uncertain time-varying delays,” IEEE Transactions on Automatic Control, vol. 54, no. 7, pp. 1575–1579, 2009.
  • L. Qiu, B. Xu, and S. Li, “Guaranteed cost control for discrete-time networked control systems with random Markov delays,” Journal of Systems Engineering and Electronics, vol. 22, no. 4, pp. 661–671, 2011.
  • E. C. Martins and F. G. Jota, “Design of networked control systems with explicit compensation for time-delay variations,” IEEE Transactions on Systems, Man and Cybernetics C, vol. 40, no. 3, pp. 308–318, 2010.
  • I. Pan, S. Das, and A. Gupta, “Tuning of an optimal fuzzy PID controller with stochastic algorithms for networked control systems with random time delay,” ISA Transactions, vol. 50, no. 1, pp. 28–36, 2011.
  • L. Qiu, B. Xu, and S. Li, “${H}_{2}$/${H}_{\infty }$ control of networked control system with random time delays,” Science China. Information Sciences, vol. 54, no. 12, pp. 2615–2630, 2011.
  • Y. Ishido, K. Takaba, and D. E. Quevedo, “Stability analysis of networked control systems subject to packet-dropouts and finite-level quantization,” Systems & Control Letters, vol. 60, no. 5, pp. 325–332, 2011.
  • Y. Tang, H. J. Gao, W. Zou, and J. Kurths, “Distributed synchronization in networks of agent systems with nonlinearities and random switchings,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 43, pp. 358–370, 2013.
  • Z.-H. Guan, C.-Y. Chen, G. Feng, and T. Li, “Optimal tracking performance limitation of networked control systems with limited bandwidth and additive colored white Gaussian noise,” IEEE Transactions on Circuits and Systems I, vol. 60, no. 1, pp. 189–198, 2013.
  • J. Yu, L. Wang, and M. Yu, “Switched system approach to stabilization of networked control systems,” International Journal of Robust and Nonlinear Control, vol. 21, no. 17, pp. 1925–1946, 2011.
  • T. Suzuki, M. Kono, N. Takahashi, and O. Sato, “Controllability and stabilizability of a networked control system with periodic communication constraints,” Systems & Control Letters, vol. 60, no. 12, pp. 977–984, 2011.
  • D. Wu, J. Wu, S. Chen, and J. Chu, “Stability of networked control systems with polytopic uncertainty and buffer constraint,” IEEE Transactions on Automatic Control, vol. 55, no. 5, pp. 1202–1208, 2010.
  • B. Zhu and K. Xia, “Design of subsidence monitoring system based on wireless sensor networks,” in Proceedings of the 6th International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM '10), pp. 1–4, September 2010.
  • Y. Xia, L. Li, G.-P. Liu, and P. Shi, “${H}_{\infty }$ predictive control of networked control systems,” International Journal of Control, vol. 84, no. 6, pp. 1080–1097, 2011.
  • P. Wang, C. Han, and B. Ding, “Stability of discrete-time networked control systems and its extension for robust ${H}_{\infty }$ control,” International Journal of Systems Science, vol. 44, no. 2, pp. 275–288, 2013.
  • X. Tang and B. Ding, “Model predictive control of linear systems over networks with data quantizations and packet losses,” Automatica, vol. 49, no. 5, pp. 1333–1339, 2013.
  • N. Xie and B. Xia, “Robust fault tolerant controller design for uncertain networked control systems with fast-varying delay and packet-dropout,” in Proceedings of the 6th International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM '10), pp. 1–4, September 2010.
  • W.-A. Zhang and L. Yu, “Modelling and control of networked control systems with both network-induced delay and packet-dropout,” Automatica, vol. 44, no. 12, pp. 3206–3210, 2008.
  • B. Yu and Y. Shi, “State feedback stabilization of networked control systems with random time delays and packet dropout,” in Proceedings of the ASME Dynamic Systems and Control Conference (DSCC '08), pp. 1–7, October 2008.
  • H. Dong, Z. Wang, and H. Gao, “Robust ${H}_{\infty }$ filtering for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts,” IEEE Transactions on Signal Processing, vol. 58, no. 4, pp. 1957–1966, 2010.
  • C. Jiang, D. X. Zou, and Q. L. Zhang, “Observer-based control for networked control systems with network induced delay and packet dropout,” in Proceedings of the 8th World Congress on Intelligent Control and Automation (WCICA '10), pp. 4376–4379, July 2010.
  • X. Li, X. Wu, Z. Xu, and C. Huang, “Fault detection observer design for networked control system with long time-delays and data packet dropout,” Journal of Systems Engineering and Electronics, vol. 21, no. 5, pp. 877–882, 2010.
  • S. B. Li, Y. Q. Wang, F. Xia et al., “Guaranteed cost control of networked guaranteed cost control of networked control systems with time-delays and packet losses,” International Journal of Wavelets, Multiresolution and Information Processing, vol. 4, no. 4, pp. 691–7066, 2006.
  • Y.-L. Wang and G.-H. Yang, “Time delay and packet dropout compensation for networked control systems: a linear estimation method,” International Journal of Control, vol. 83, no. 1, pp. 115–124, 2010.
  • A. Liu, L. Yu, and W. Zhang, “One-step receding horizon ${H}_{\infty }$ control for networked control systems with random delay and packet disordering,” ISA Transactions, vol. 50, no. 1, pp. 44–52, 2011.
  • L. Qiu, Q. Luo, F. Gong, S. B. Li, and B. G. Xu, “Stability and stabilization of networked control systems with random time delays and packet dropouts,” Journal of the Franklin Institute, vol. 350, no. 7, pp. 1886–1907, 2013.
  • Y. Sun and Y. Huo, “Robust static output feedback control for networked control system with random time delay,” in Proceedings of the 2nd International Conference on Advanced Computer Control (ICACC '10), pp. 547–551, March 2010.
  • C. Peng, Y. Tian, and D. Yue, “Output feedback control of discrete-time systems in networked environments,” IEEE Transactions on Systems, Man, and Cybernetics A, vol. 41, no. 1, pp. 185–190, 2011.