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Random stabilization of sampled-data control systems with nonuniform sampling

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Abstract

For a sampled-data control system with nonuniform sampling, the sampling interval sequence, which is continuously distributed in a given interval, is described as a multiple independent and identically distributed (i.i.d.) process. With this process, the closed-loop system is transformed into an asynchronous dynamical impulsive model with input delays. Sufficient conditions for the closed-loop mean-square exponential stability are presented in terms of linear matrix inequalities (LMIs), in which the relation between the nonuniform sampling and the mean-square exponential stability of the closed-loop system is explicitly established. Based on the stability conditions, the controller design method is given, which is further formulated as a convex optimization problem with LMI constraints. Numerical examples and experiment results are given to show the effectiveness and the advantages of the theoretical results.

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References

  1. X. M. Tang, B. C. Ding. Design of networked control systems with bounded arbitrary time delays. International Journal of Automation and Computing, vol. 9, no. 2, pp. 182–190, 2012.

    Article  Google Scholar 

  2. M. Y. Zhao, H. P. Liu, Z. J. Li, D. H. Sun. Fault tolerant control for networked control systems with packet loss and time delay. International Journal of Automation and Computing, vol. 8, no. 2, pp. 244–253, 2011.

    Article  Google Scholar 

  3. T. W. Chen, B. A. Francis. Optimal Sampled-data Control Systems, London, England: Springer, 1995.

    Book  MATH  Google Scholar 

  4. J. Nilsson, B. Bernhardsson, B. Wittenmark. Stochastic analysis and control of real-time systems with random time delays. Automatica, vol. 34, no. 1, pp. 57–64, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  5. W. Zhang, M. S. Branicky, S. M. Phillips. Stability of networked control systems. IEEE Control Systems Magazine, vol. 21, no. 1, pp. 84–99, 2001.

    Article  Google Scholar 

  6. Y. S. Suh. Stability and stabilization of nonuniform sampling systems. Automatica, vol. 44, no. 12, pp. 3222–3226, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  7. H. Fujioka. A discrete-time approach to stability analysis of systems with aperiodic sample-and-hold devices. IEEE Transactions on Automatic Control, vol. 54, no. 10, pp. 2440–2445, 2009.

    Article  MathSciNet  Google Scholar 

  8. Y. Oishi, H. Fujioka. Stability and stabilization of aperiodic sampled-data control systems using robust linear matrix inequalities. Automatica, vol. 46, no. 8, pp. 1327–1333, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. L. Xiong, J. Lam. Stabilization of linear systems over networks with bounded packet loss. Automatica, vol. 43, no. 1, pp. 80–87, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  10. E. Fridman, A. Seuret, J. P. Richard. Robust sampled-data stabilization of linear systems: An input delay approach. Automatica, vol. 40, no. 8, pp. 1441–1446, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  11. D. Yue, Q. L. Han, C. Peng. State feedback controller design of networked control systems. IEEE Transactions on Circuits and Systems, Part II: Express Briefs, vol. 51, no. 11, pp. 640–644, 2004.

    Article  Google Scholar 

  12. B. Tang, G. P. Liu, W. H. Gui. Improvement of state feedback controller design for networked control systems. IEEE Transactions on Circuits and Systems, Part II: Express Briefs, vol. 55, no. 5, pp. 464–468, 2008.

    Article  Google Scholar 

  13. H. J. Gao, T. W. Chen, J. Lam. A new delay system approach to network-based control. Automatica, vol. 44, no. 1, pp. 39–52, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  14. X. F. Jiang, Q. L. Han, S. R. Liu, A. K. Xue. A new H ∞ stabilization criterion for networked control systems. IEEE Transactions on Automatic Control, vol. 53, no. 4, pp. 1025–1032, 2008.

    Article  MathSciNet  Google Scholar 

  15. M. Yu, L. Wang, T. G. Chu, F. Hao. Stabilization of networked control systems with data packet dropout and transmission delays: Continuous-time case. European Journal of Control, vol. 11, pp. 40–49, 2005.

    Article  MathSciNet  Google Scholar 

  16. L. Mirkin. Some remarks on the use of time-varying delay to model sample-and-hold circuits. IEEE Transactions on Automatic Control, vol. 52, no. 6, pp. 1109–1112, 2007.

    Article  MathSciNet  Google Scholar 

  17. H. Fujioka. Stability analysis of systems with aperiodic sample-and-hold devices. Automatica, vol. 45, no. 3, pp. 771–775, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  18. L. S. Hu, J. Lam, Y. Y. Cao, H. H. Shao. A linear matrix inequality (LMI) approach to robust H 2 sampled-data control for linear uncertain systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 33, no. 1, pp. 149–155, 2003.

    Article  Google Scholar 

  19. P. Naghshtabrizi, J. P. Hespanha, A. R. Teel. Exponential stability of impulsive systems with application to uncertain sampled-data systems. Systems & Control Letters, vol. 57, no. 5, pp. 378–385, 2008.

    Article  MathSciNet  MATH  Google Scholar 

  20. E. Fridman. A refined input delay approach to sampleddata control. Automatica, vol. 46, no. 2, pp. 421–427, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  21. W. A. Zhang, 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.

    Article  Google Scholar 

  22. R. Wang, B. Wang, G. P. Liu, W. Wang, D. Rees. H ∞ controller design for networked predictive control systems based on the average dwell-time approach. IEEE Transactions on Circuits and Systems, Part II: Express Briefs, vol. 57, no. 4, pp. 310–314, 2010.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Automation, Guangdong University of Technology, Guangzhou, 510006, China

    Bin Tang, Qi-Jie Zeng, De-Feng He & Yun Zhang

Authors
  1. Bin Tang
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  2. Qi-Jie Zeng
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  3. De-Feng He
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  4. Yun Zhang
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Corresponding author

Correspondence to Bin Tang.

Additional information

This work was supported by National Natural Science Foundation of China (Nos. 61104105, U0735003 and 60974047) and Natural Science Foundation of Guangdong Province of China (No. 9451009001002702).

Bin Tang graduated from Xiangtan University, China in 2001. He received the M. Eng. degree and the Ph.D. degree from Central South University, China in 2004 and 2008, respectively. He is currently an associate professor in the Faculty of Automation, Guangdong University of Technology, China.

His research interests include networked control systems, sampled-data control systems, and delay systems.

Qi-Jie Zeng graduated from South China University of Science and Technology, China in 2000. He received the M. Sc. degree from the South China University of Science and Technology, China in 2003. He is currently a lecturer and a Ph.D. candidate in Department of Automation, Guangdong University of Technology, China.

His research interests include networked control, robotics, neural networks, robust control, and intelligent systems.

De-Feng He graduated from Zhoukou Normal University, China in 2011. He is currently a M.Eng. candidate in the Faculty of Automation, Guangdong University of Technology, China.

His interest is networked control systems.

Yun Zhang graduated from Hunan University, China in 1982. He received the M. Sc. degree from Hunan University, China in 1986 and the Ph.D. degree from South China University of Science and Technology, China in 1998. He is currently a professor in Department of Automation, Guangdong University of Technology, China.

His research interests include intelligent control systems, network systems, and signal processing.

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Tang, B., Zeng, QJ., He, DF. et al. Random stabilization of sampled-data control systems with nonuniform sampling. Int. J. Autom. Comput. 9, 492–500 (2012). https://doi.org/10.1007/s11633-012-0672-y

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  • DOI: https://doi.org/10.1007/s11633-012-0672-y

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