Dynamic Output Feedback H Control for Linear Parameter-varying Systems with Time-delay

Abstract

In this paper, we address a synthesis problem of the parameter-dependent output feedback H control for linear parameter-varying systems with time-delay. The scheme adopts the parameter-dependent past state information to construct the dynamic output feedback controller. In this case, on basis of the quadratic Lyapunov functional with parameter-dependence, we analyze the parameter-dependent H stability conditions for the closed-loop time-delayed linear parameter-varying system in terms of linear matrix inequalities. However, this stability condition is of an infinite-dimension. To derive computationally tractable criteria for the dynamic output feedback controller, several slack variables and a convex relaxation technique are employed to have the infinite-dimensional condition of linear matrix inequalities cast into a finite dimensional convex optimization problem. By solving the convex optimization problem, we harvest the dynamic output feedback controller with memory for the time-delayed linear parameter-varying system. Finally, two examples are included to illustrate the effectiveness of the proposed approach.

This is a preview of subscription content, log in to check access.

References

  1. [1]

    M. X. Li, Y. M. Jia, and J. P. Du, “LPV control with decoupling performance of 4WS vehicles under velocity-varying motion,” IEEE Transactions on Control Systems Technology, vol. 22, no. 5, pp. 1708–1724, 2014.

    Google Scholar 

  2. [2]

    S. M. Hashemi, H. S. Abbas, and H. Werner, “Low-complexity linear parameter-varying modeling and control of a robotic manipulator,” Control Engineering Practice, vol. 20, no. 3, pp. 248–257, 2012.

    Google Scholar 

  3. [3]

    C. F. Hu, X. F. Wei, and Y. L. Ren, “Passive fault-tolerant control based on weighted LPV tube-MPC for air-breathing hypersonic vehicles,” International Journal of Control, Automation, and Systems, vol. 17, no. 8, pp. 1957–1970, 2019.

    Google Scholar 

  4. [4]

    W. Xie, “H2 gain scheduled state feedback for LPV system with new LMI formulation,” Control Theory and Applications, IEEProceedings, vol. 152, no. 6, pp. 693–697, 2005.

    Google Scholar 

  5. [5]

    M. M. Seron and J. A. D. Doná, “Robust fault estimation and compensation for LPV systems under actuator and sensor faults,” Automatica, vol. 52, no. 52, pp. 294–301, 2015.

    MathSciNet  MATH  Google Scholar 

  6. [6]

    G. Benjamin, S. A. Harouna, Z. Michel, and D. Mohamed, “LPV approach for H filter design for a class of nonlinear systems,” IFAC Proceedings Volumes, vol. 41, no. 2, pp. 11497–11502, 2008.

    Google Scholar 

  7. [7]

    R. Houimli, N. Bedioui, and M. Besbes, “An improved polytopic adaptive LPV observer design under actuator fault,” International Journal of Control, Automation, and Systems, vol. 16, no. 1, pp. 1957–1970, 2019.

    Google Scholar 

  8. [8]

    G. B. Cai, C. H. Hu, B. J. Yin, and H. F. He, “Gain-Scheduled H2 controller synthesis for continuous-time polytopic LPV systems,” Mathematical Problems in Engineering, no. 1, pp. 1–14, 2014.

    Google Scholar 

  9. [9]

    J. Bai, R. Lu, L. Xia, A. Xue, and Z. Shi, “Fuzzy regional pole placement based on fuzzy Lyapunov functions,” Neurocomputing, vol. 167, no. C, pp. 467–473, 2015.

    Google Scholar 

  10. [10]

    K. Q. Gu, V. L. Kharitonov, and J. Chen, Stability of Time-delay Systems, Birkhuser, Boston, MA, USA, 2003.

    Google Scholar 

  11. [11]

    E. Fridman and U. Shaked, “A descriptor system approach to H control of linear time-delay systems,” IEEE Transactions on Automatic Control, vol. 47, no. 2, pp. 253–270, Feb. 2002.

    MathSciNet  MATH  Google Scholar 

  12. [12]

    M. Wu, Y. He, J. H. She, and G. P. Liu, “Delay-dependent criteria for robust stability of time-varying delay systems,” Automatica, vol. 40, no. 8, pp. 1435–1439, 2004.

    MathSciNet  MATH  Google Scholar 

  13. [13]

    H. Shen, Z. G. Huang, J. D. Cao, and J. H. Park, “Exponential H filtering for continuous-time switched neural networks under persistent dwell-time switching regularity,” IEEE Transactions on Cybernetics, 2019. DOI: https://doi.org/10.1109/TCYB.2019.2901867

  14. [14]

    H. H. Lian, S. P. Xiao, Z. Wang, X. H. Zhang, and H. Q. Xiao, “Further results on sampled-data synchronization control for chaotic neural networks with actuator saturation,” Neurocomputing, vol. 346, pp. 30–37, Jun. 2019.

    Google Scholar 

  15. [15]

    L. Zhang, Q. L. Han, X. M. Zhang, and X. H. Yu, “Sliding mode control with mixed current and delayed states for offshore steel jacket platforms,” IEEE Transactions on Control Systems Technology, vol. 22, no. 5, pp. 1769–1783, May 2014.

    Google Scholar 

  16. [16]

    H. B. Zeng, Z. L. Zhai, Y. He, K. L. Teo, and W. Wang, “New insights on stability of sampled-data systems with time-delay,” Applied Mathematics and Computation, vol. 374, pp. 125041, 2020.

    MathSciNet  MATH  Google Scholar 

  17. [17]

    A. Seuret and F. Gouaisbaut, “Hierarchy of LMI conditions for the stability analysis of time-delay systems,” Systems & Control Letters, vol. 81, pp. 1–7, 2015.

    MathSciNet  MATH  Google Scholar 

  18. [18]

    X. M. Zhang, Q. L. Han, A. Seuret, F. Gouaisbaut, and Y. He, “An overview of recent advances in stability of linear systems with time-varying delays,” IET Control Theory Appl., vol. 13, no. 1, pp. 1–16, Jan 2019.

    MathSciNet  MATH  Google Scholar 

  19. [19]

    H. B. Zeng, Y. He, M. Wu, and J. H. She, “Free-matrix-based integral inequality for stability analysis of systems with time-varying delay,” IEEE Transactions on Automatic Control, vol. 60, no. 10, pp. 2768–2772, 2015.

    MathSciNet  MATH  Google Scholar 

  20. [20]

    C. K. Zhang, Y. He, L. Jiang, and M. Wu, “Notes on stability of time-delay systems: bounding inequalities and augmented Lyapunov-Krasovskii functionals,” IEEE Transactions on Automatic Control, vol. 62, pp. 5331–5336, 2017.

    MathSciNet  MATH  Google Scholar 

  21. [21]

    H. B. Zeng, X. G. Liu, and W. Wang, “A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems,” Applied Mathematics and Computation, vol. 354, pp. 1–8, 2019.

    MathSciNet  MATH  Google Scholar 

  22. [22]

    H. B. Zeng, Y. He, M. Wu, and J. H. She, “New results on stability analysis for systems with discrete distributed delay,” Automatica, vol. 60, pp. 189–192, 2015.

    MathSciNet  MATH  Google Scholar 

  23. [23]

    C. Briat, Linear Parameter-varying and Time-delay Systems. Advances in Delays and Dynamics, Springer Berlin Heidelberg, ed: Berlin, Heidelberg, 2015.

  24. [24]

    F. Wu and K. M. Grigoriadis, “LPV Systems with parameter-varying time delays: analysis and control,” Automatical, vol. 37, no. 2, pp. 221–229, 2001.

    MathSciNet  MATH  Google Scholar 

  25. [25]

    X. Zhang, P. Tsiotras, and C. Knospe, “Stability analysis of LPV time-delayed systems,” International Journal of Control, vol. 75, no. 7, pp. 538–558, 2002.

    MathSciNet  MATH  Google Scholar 

  26. [26]

    H. Shen, Y. Z. Men, J. D. Cao, and J. H. Park, “H filtering for fuzzy jumping genetic regulatory networks with round-robin protocol: A hidden-Markov-model-based approach,” IEEE Transactions on Fuzzy Systems, vol. 28, no. 1, pp. 112–121, 2020.

    Google Scholar 

  27. [27]

    Y. D. Wang, J. W. Xia, Z. Wang, and H. Shen, “Design of a fault-tolerant output-feedback controller for thickness control in cold rolling mills,” Applied Mathematics and Computation, vol. 369, Article ID 124841, 2019.

  28. [28]

    X. M. Zhang, W. U. Min, and H. E. Yong, “Delay dependent robust control for linear systems with multiple time-varying delays and uncertainties,” Control & Decision, vol. 19, no. 5, pp. 496–500, 2004.

    MathSciNet  MATH  Google Scholar 

  29. [29]

    M. H. Wang, G. Liu, and S. Yang, “Polytopic-LPV-system-based control design for hypersonic vehicle,” Aerospace Control & Application, vol. 39, no. 1, pp. 15–23, 2013.

    Google Scholar 

  30. [30]

    S. L. Chen, Y. Yu, Z. Kai, and M. Jie, “Stabilizing a class of uncertain switched linear systems via observer-based output feedback,” Proceedings of the 27th Chinese Control Conference, Kunming, China, 2008.

  31. [31]

    J. Li and Y. Z. Li, “Stabilization of a class of discrete-time switched systems via observer-based output feedback,” Journal of Control Theory & Applications, vol. 5, no. 3, pp. 307–311, 2007.

    MathSciNet  Google Scholar 

  32. [32]

    Y. F. Li, “Design of H static output feedback control for discrete-time systems with limited actuator,” Asian Journal of Control, vol. 17, no. 1, pp. 284–296, 2015.

    MathSciNet  MATH  Google Scholar 

  33. [33]

    H. Zhang, H. Fan, and S. Ma, “Robust output feedback stabilization for uncertain discrete-time Markov jump singular systems,” Journal of Shandong University, vol. 47, no. 1, pp. 62–71, 76, 2012.

    MathSciNet  MATH  Google Scholar 

  34. [34]

    Z. G. Zhang, C. H. Zhang, and J. Feng, “Delay-dependent H dynamic output feedback control for linear systems with time-varying delayed state,” Journal of Shandong University, vol. 40, no. 1, pp. 51–56, 2005.

    Google Scholar 

  35. [35]

    L. Song and J. Y. Yang, “An improved approach to robust stability analysis and controller synthesis for LPV systems,” International Journal of Robust & Nonlinear Control, vol. 21, no. 13, pp. 1574–1586, 2011.

    MathSciNet  MATH  Google Scholar 

  36. [36]

    L. Lv and Z. S. Li, “Design of robust H controller for uncertain systems with time-varying delay-LMI approach,” Computing Technology and Automation, vol. 25, no. 1, pp. 4–7, 2006.

    Google Scholar 

  37. [37]

    K. Hu and J. Yuan, “Improved robust H1 filtering for uncertain discrete-time switched systems,” IET Control Theory and Applications, vol. 3, no. 3, pp. 315–324, 2009.

    MathSciNet  Google Scholar 

  38. [38]

    W. Jiang, H. L. Wang, J. H. Lv, W. W. Qin, and G. B. Cai, “Gain-scheduled H/H2 output feedback controller synthesis for continuous-time polytopic linear parameter varying systems,” Control Theory & Applications, vol. 33, no. 9, pp. 1225–1235, 2016.

    MATH  Google Scholar 

  39. [39]

    K. Tan, K. Grigoriadis, and F. Wu, “H and L2 — toL∞ gain control of linear parameter-varying systems with parameter-varying delays,” IEE Proceedings-Control Theory and Applications, vol. 150, no. 5, pp. 509–517, 2003.

    Google Scholar 

  40. [40]

    I. Nejem, H. B. Mohamed, and B. Faouzi, “Robust control of delayed LPV systems via parameter-dependent Lyapunov functionals,” Proc. of 15th International Multi-Conference on Systems, Signals & Devices, Tunisia, Hammamet, 2018.

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jinjie Huang.

Additional information

Recommended by Associate Editor Young Ik Son under the direction of Editor PooGyeon Park.

Jinjie Huang received his B.S. and M.S. degrees in automatic control from Harbin University of Science and Technology, Harbin, China, in 1990 and 1997, respectively, and a Ph.D. degree in control theory and control engineering from Harbin Institute of Technology, Harbin, China, in 2004. He is currently a full professor with the School of Automation and the School of Computer Science and Technology, Harbin University of Science and Technology, Harbin, China. His research interests include linear system control, network control system, nonlinear control system.

Xiaozhen Pan received her B.S. and M.S. degrees in automatic control from Harbin University of Science and Technology, Harbin, China, in 2014 and 2017, respectively, where she is currently working towards her Ph.D. degree. Her research interests include event-triggered control, robust control, and LPV system.

Xianzhi Hao received his B.S. and M.S. degrees in automatic control from Harbin University of Science and Technology, Harbin, China, in 2015 and 2017, respectively, where he is currently working towards his Ph.D. degree. His research interests include switching control, robust control, switched system and positive linear system.

Wanda Putra received his B.Eng. degree in Informatic Engineering and M.Eng. degree in Information Technology from Gadjah Mada University in 2015. Since August 2016, he is with the School of Computer Science and Technology from Harbin University of Science and Technology as a Ph.D. candidate. His research interests include mobile computing and network security.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Huang, J., Pan, X., Hao, X. et al. Dynamic Output Feedback H Control for Linear Parameter-varying Systems with Time-delay. Int. J. Control Autom. Syst. (2020). https://doi.org/10.1007/s12555-019-0792-z

Download citation

Keywords

  • H control
  • linear matrix inequality
  • linear parameter-varying system
  • memory output feedback
  • time-delayed system