Skip to main content
SpringerLink
Log in

Output Feedback H ∞ Control for 2-D State-Delayed Systems

  • Published:
Circuits, Systems & Signal Processing Aims and scope Submit manuscript

Abstract

In this paper, we consider a class of two-dimensional (2-D) local state-space (LSS) Fornasini–Marchesini (FM) second models with delays in the states, and we study delay-independent and delay-dependent H ∞ control problems via output feedback. First, based on the definition of H ∞ disturbance attenuation γ for 2-D state-delayed systems, we propose a delay-dependent bounded real lemma. Specifically, a new Lyapunov functional candidate is introduced and free-weighting matrices are added to the difference Lyapunov functional for 2-D systems possessing two directions. Then delay-independent and delay-dependent output feedback H ∞ controllers are developed that ensure that the closed-loop system is asymptotically stable and has H ∞ performance γ in terms of linear matrix inequality (LMI) feasibility. Furthermore, the minimum H ∞ norm bound γ is obtained by solving linear objective optimization problems. Numerical examples demonstrate the effectiveness and advantages of the LMI approach to H ∞ control problems for 2-D state-delayed systems.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Basin, E. Sanchez, R. Martinez-Zuniga, Optimal linear filtering for systems with multiple state and observation delays. Int. J. Innov. Comput. Inf. Control 3, 1309–1320 (2007)

    Google Scholar 

  2. S.-F. Chen, I.-K. Fong, Robust filtering for 2-D state-delayed systems with nft uncertainties. IEEE Trans. Signal Process. 54(1), 274–285 (2006)

    Article  Google Scholar 

  3. C. Du, L. Xie, C. Zhang, H ∞ control and robust stabilization of two-dimensional system in Roesser models. Automatica 37(2), 205–211 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. E. Fridman, U. Shaked, An improved stabilization method for linear time-delay systems. IEEE Trans. Autom. Control 47(11), 1931–1937 (2002)

    Article  MathSciNet  Google Scholar 

  5. K. Galkowski, E. Rogers, W. Paszke, D. Owens, Linear repetitive process control theory applied to a physical example. Appl. Math. Comput. Sci. 13(1), 87–99 (2003)

    MATH  MathSciNet  Google Scholar 

  6. H. Gao, T. Chen, New results on stability of discrete-time systems with time-varying state delay. IEEE Trans. Autom. Control 52(2), 328–334 (2007)

    Article  MathSciNet  Google Scholar 

  7. X. Guan, C. Long, G. Duan, Robust optimal guaranteed cost control for 2-D discrete systems. IEE Proc. Control Theory Appl. 148(5), 355–361 (2001)

    Article  Google Scholar 

  8. Y. He, Q.-G. Wang, L. Xie, C. Lin, Further improvement of free-weighting matrices technique for systems with time-varying delay. IEEE Trans. Autom. Control 52(2), 293–299 (2007)

    Article  MathSciNet  Google Scholar 

  9. Y. He, M. Wu, J. She, G. Liu, Delay-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties. IEEE Trans. Autom. Control 49, 828–832 (2004)

    Article  MathSciNet  Google Scholar 

  10. X. Jiang, Q. Han, Delay-dependent robust stability for uncertain linear systems with internal time-varying delay. Automatica 42(6), 1059–1065 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  11. T. Katayama, M. Kosaka, Recursive filtering algorithm for a 2-D system. IEEE Trans. Autom. Control 24, 130–132 (1979)

    Article  MATH  Google Scholar 

  12. C. Lin, Q.-G. Wang, T.H. Lee, A less conservative robust stability test for linear uncertain time-delay systems. IEEE Trans. Autom. Control 51(1), 87–91 (2006)

    Article  MathSciNet  Google Scholar 

  13. M. Mahmoud, Y. Shi, H. Nounou, Resilient observer-based control of uncertain time-delay systems. Int. J. Innov. Comput. Inf. Control 3(2), 407–418 (2007)

    Google Scholar 

  14. W. Paszke, J. Lam, K. Galkowski, S. Xu, Z. Lin, Robust stability and stabilisation of 2-D discrete state-delayed systems. Syst. Control Lett. 51, 278–291 (2004)

    Article  MathSciNet  Google Scholar 

  15. W. Paszke, J. Lam, K. Galkowski, S. Xu, E. Rogers, H ∞ control of 2-D linear state-delayed systems, in The 4th IFAC Workshop on Time-Delay Systems, Rocquencourt, France, September 2003, pp. 8–10

  16. D. Peng, X. Guan, C. Long, Robust output feedback guaranteed cost control for 2-D uncertain state-delayed systems. Asian J. Control 9(4), 470–474 (2007)

    MathSciNet  Google Scholar 

  17. R. Wang, J. Zhao, Exponential stability analysis for discrete-time switched linear systems with time-delay. Int. J. Innov. Comput. Inf. Control 3, 1557–1564 (2007)

    Google Scholar 

  18. Y. Wang, Z. Sun, H-Infinite control of networked control system via LMI approach. Int. J. Innov. Comput. Inf. Control 3, 343–352 (2007)

    Article  Google Scholar 

  19. L. Wu, P. Shi, H. Gao, C. Wang, H ∞ mode reduction for two-dimensional discrete state-delayed systems. IEE Proc. Vis. Image Signal Process. 153(6), 769–784 (2006)

    Article  MathSciNet  Google Scholar 

  20. L. Wu, Z. Wang, H. Gao, C. Wang, Filtering for uncertain two-dimensional discrete systems with state delays. Signal Process. 87(9), 2213–2230 (2007)

    Article  Google Scholar 

  21. S. Xu, J. Lam, Improved delay-dependent stability criteria for time-delay systems. IEEE Trans. Autom. Control 50(3), 384–387 (2005)

    Article  MathSciNet  Google Scholar 

  22. J. Yee, G. Yang, J. Wang, Reliable output-feedback controller design for discrete-time linear systems: an iterative LMI approach, in Proceedings of American Control Conference, 2001

Download references

Author information

Authors and Affiliations

  1. College of Science, Yanshan University, Qinhuangdao, 066004, China

    Dan Peng

  2. Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, China

    Xinping Guan

Authors
  1. Dan Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xinping Guan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dan Peng.

Additional information

This work was supported in part by the National Natural Science Foundation of China (60525303 and 60604004), NSF of Hebei Province (08M008) and the Key Scientific Research Project of the Education Ministry (204014).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Peng, D., Guan, X. Output Feedback H ∞ Control for 2-D State-Delayed Systems. Circuits Syst Signal Process 28, 147–167 (2009). https://doi.org/10.1007/s00034-008-9074-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-008-9074-3

Keywords

Search

Navigation