Skip to main content
SpringerLink
Log in

H∞ Filtering for a Class of Singular Time-delay Systems

  • Regular Papers
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper describes the H∞ filtering problem for a class of nonlinear singular time-delay systems. A sufficient condition for the existence of H∞ filter is given. Based on the Cayley-Hamilton Theorem and Lyapunov stability theory, the H∞ filter is designed such that the filtering error is asymptotically stable and satisfies the prescribed H∞ performance. In terms of linear matrix inequality, a sufficient condition for the solvability of the addressed problem is obtained. Finally, some numerical examples are employed to demonstrate the effectiveness of the proposed approaches.

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. Chadli and M. Darouach, “Robust admissibility of uncertain switched singular systems,” International Journal of Control, vol. 84, no. 10, pp. 1587–1600, October 2011.

    Article  MathSciNet  MATH  Google Scholar 

  2. J. Wang, S. Ma, C. Zhang, and M. Fu, “H ∞ state estimation via asynchronous filtering for descriptor Markov jump systems with packet losses,” Signal Processing, vol. 154, pp. 159–167, January 2019.

    Article  Google Scholar 

  3. J. Zhang, F. Zhu, H. R. Karimi, and F. Wang, “Observer-based Sliding Mode Control for T-S Fuzzy Descriptor Systems with Time-delay,” IEEE Transactions on Fuzzy Systems, 2019. DOI: 10.1109/TFUZZ.2019.2893220

    Google Scholar 

  4. M. Darouach and M. Chadli, “Admissibility and control of switched discrete-time singular systems,” Systems Science & Control Engineering: An Open Access Journal, vol. 1, no. 1, pp. 43–51, 2013.

    Article  Google Scholar 

  5. M. Chadli, P. Shi, Z. Feng, and J. Lam, “New bounded real lemma formulation and control for continuous-time descriptor systems,” Asian Journal of Control, vol. 19, no. 6, pp. 2192–2198, November 2017.

    Article  MathSciNet  MATH  Google Scholar 

  6. D. Simon, “Kalman filtering with state constraints: a survey of linear and nonlinear algorithms,” IET Control Theory & Applications, vol. 4, no. 8, pp. 1303–1318, January 2010.

    Article  MathSciNet  Google Scholar 

  7. S. M. Lee, D. H. Ji, O. M. Kwon, and J. H. Park, “Robust H ∞ filtering for a class of discrete-time nonlinear systems,” Applied Mathematics and Computation, vol. 217, no. 20, pp. 7991–7997, June 2011.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. C. Geromel and M. C. De Oliveria, “H 2 and H ∞ robust filtering for convex bounded uncertain systems,” IEEE Transactions on Automatic Control, vol. 46, no. 1, pp. 100–107, January 2001.

    Article  MathSciNet  Google Scholar 

  9. L. Caraffa, J. P. Tarel, and P. Charbonnier, “The guided bilateral filter: when the joint/cross bilateral filter becomes robust,” IEEE Transactions on Image Processing, vol. 24, no. 4, pp. 1199–1208, April 2015.

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Elsayed and M. J. Grimble, “A new approach to H ∞ design of optimal digital linear filters,” IMA Journal of Mathematical Control & Information, vol. 6, no. 2, pp. 233–251, June 1989.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. Y. An, G. L. Wen, N. F. Gan, and R. F. Li, “A delay derivative-dependent approach to robust H ∞ filter design for uncertain systems with time-varying distributed delays,” Journal of the Franklin Institute, vol. 348, no. 2, pp. 179–200, March 2011.

    Article  MathSciNet  MATH  Google Scholar 

  12. M. Abbaszadeha and H. J. Marquez, “A generalized framework for robust nonlinear H ∞ filtering of Lipschitz descriptor systems with parametric and nonlinear uncertainties,” Automatica, vol. 48, no. 5, pp. 894–900, May 2012.

    Article  MathSciNet  MATH  Google Scholar 

  13. X. He, Z. D. Wang, and D. H. Zhou, “Robust H ∞ filtering for networked systems with multiple state delays,” International Journal of Control, vol. 80, no. 8, pp. 1217–1232, August 2007.

    Article  MathSciNet  MATH  Google Scholar 

  14. G. H. Yang, “Insensitive H ∞ filter design for continuous-time systems with respect to filter coefficient variations,” Automatica, vol. 46, no. 11, pp. 1860–1869, November 2010.

    Article  MathSciNet  MATH  Google Scholar 

  15. Z. G. Wu, S. Dong, P. Shi, D. Zhang, and T. Huang, “Reliable Filter Design of Takagi-Sugeno Fuzzy Switched Systems With Imprecise Modes,” IEEE Transactions on Cybernetics, 2019. DOI: 10.1109/TCYB.2018.2885505

    Google Scholar 

  16. Y. M. Li and S. C. Tong, “Prescribed performance adaptive fuzzy output-feedback dynamic surface control for nonlinear large-scale systems with time delays,” Information Sciences, vol. 292, pp. 125–142, January 2015.

    Article  MathSciNet  MATH  Google Scholar 

  17. Y. M. Li, S. C. Tong, and T. S. Li, “Hybrid fuzzy adaptive output feedback control design for uncertain MIMO nonlinear systems with time-varying delays and input saturation,” IEEE Transactions on Fuzzy Systems, vol. 24, no. 4, pp. 841–853, August 2016.

    Article  Google Scholar 

  18. M. Malek-Zavarei and M. Jamshidi, Time-delay Systems: Analysis, Optimization and Applications, North-Holland, 1987.

    MATH  Google Scholar 

  19. S. I. Niculescu, Delay Effects on Stability: A Robust Control Approach, Springer Science & Business Media, 2001.

    MATH  Google Scholar 

  20. H. Que, M. Fang, Z.-G. Wu, H. Su, T. Huang, and D. Zhang, “Exponential synchronization via aperiodic sampling of complex delayed networks,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 49, no. 7, pp. 1399–1407, July 2019.

    Article  Google Scholar 

  21. X. W. Li, H. J. Gao, and K. Q. Gu, “Delay-independent stability analysis of linear time-delay systems based on frequency discretization,” Automatica, vol. 70, pp. 288–294, August 2016.

    Article  MathSciNet  MATH  Google Scholar 

  22. H. J. Gao and C. H. Wang, “Delay-dependent robust H ∞ and L 2-L ∞ filtering for a class of uncertain nonlinear time-Delay systems,” IEEE Transactions on Automatic Control, vol. 48, no. 9, pp. 1661–1666, September 2003.

    Article  MathSciNet  MATH  Google Scholar 

  23. Z. G. Wu, H. Y. Su, and J. Chu, “Delay-dependent H ∞ filtering for singular Markovian jump time-delay systems,” Signal Processing, vol. 90, no. 6, pp. 1815–1824, June 2010.

    Article  MATH  Google Scholar 

  24. C. E. D. Souza, R. M. Palhares, and P. L. D. Peres, “Robust H ∞ filter design for uncertain linear systems with multiple time-varying state delays,” IEEE Transactions on Signal Processing, vol. 49, no. 3, pp. 569–576, March 2001.

    Article  MathSciNet  MATH  Google Scholar 

  25. S. J. Huang, X. Q. He, and N. N. Zhang, “New results on H ∞ filter design for nonlinear systems with time delay via T-S fuzzy models,” IEEE Transactions on Fuzzy Systems, vol. 19, no. 1, pp. 193–199, February 2011.

    Article  Google Scholar 

  26. M. Fang, “Synchronization for complex dynamical networks with time delay and discrete-time information,” Applied Mathematics & Computation, vol. 258, pp. 1–11, May 2015.

    Article  MathSciNet  MATH  Google Scholar 

  27. Z. G. Wu, H. Y. Su, and J. Chu, “H ∞ filtering for singular systems with time-varying delay,” International Journal of Robust & Nonlinear Control, vol. 20, no. 11, pp. 1269–1284, July 2010.

    Article  MathSciNet  MATH  Google Scholar 

  28. Y. Wang, P. Shi, Q. Wang, and D. Duan, “Exponential filtering for singular Markovian jump systems with mixed mode-dependent time-varying delay,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 60, no. 9, pp. 2440–2452, September 2013.

    Article  MathSciNet  Google Scholar 

  29. R. Lu, S. Fang, A. Xue, and H. Wu, “Quantized H ∞ filtering for singular systems,” Proc. of 3rd International Symposium on Systems & Control in Aeronautics & Astronautics. IEEE, pp. 870–874, 2010.

    Google Scholar 

  30. G. P. Lu, D. W. and C. Ho, “Full-order and reduced-order observers for lipschitz descriptor systems: the unified LMI approach,” IEEE Transactions on Circuits & Systems II Express Briefs, vol. 53, no. 7, pp. 563–567, July 2006.

  31. H. Trinh, T. Fernando, and S. Nahawandi, “Partial state observers for nonlinear systems,” IEEE Transactions on Automatic Control, vol. 51, no. 11, pp. 1808–1812, November 2006.

    Article  MathSciNet  MATH  Google Scholar 

  32. R. Lu, Y. Xu, X. Zhao, D. Pang, and A. Xue, “Delay-dependent H ∞ filtering for nonlinear singular systems with network-induced delays,” Proc. of 7th Asian Control Conference, IEEE, pp. 600–604, 2009.

    Google Scholar 

  33. S. Marir, M. Chadli, and D. Bouagada, “New admissibility conditions for singular linear continuous-time fractional-order systems,” Journal of the Franklin Institute, vol. 354, no. 2, pp. 752–766, January 2017.

    Article  MathSciNet  MATH  Google Scholar 

  34. N. Komeil and S. Masoud, “Kalman filtering for discrete-time linear fractional-order singular systems,” IET Control Theory & Applications, vol. 12, no. 9, pp. 1254–1266, December 2018.

    Article  MathSciNet  Google Scholar 

  35. S. Marir, M. Chadli, and D. Bouagada, “A novel approach of admissibility for singular linear continuous-time fractional-order systems,” International Journal of Control Automation and Systems, vol. 15, no. 2, pp. 959–964, April 2017.

    Article  MATH  Google Scholar 

  36. D. Zhai, L. W An, J. H. Li, and Q. L. Zhang, “Fault detection for stochastic parameter-varying Markovian jump systems with application to networked control systems,” Applied Mathematical Modelling, vol. 40, no. 3, pp. 2368–2383, February, 2016.

    Article  MathSciNet  Google Scholar 

  37. D. Zhai, L. W. An, D. Ye, and Q. L. Zhang, “Adaptive reliable H ∞ static output feedback control against Markovian jumping sensor failures,” IEEE Transactions on Neural Networks and Learning Systemst, vol. 29, no. 3, pp. 631–644, March 2018.

    Article  MathSciNet  Google Scholar 

  38. S. Y. Xu, T. W. Chen, and J. Lam, “Robust H ∞ filtering for uncertain Markovian jump systems with mode-dependent time delays,” IEEE Transactions on Automatic Control, vol. 48, no. 5, pp. 900–907, May 2003.

    Article  MathSciNet  MATH  Google Scholar 

  39. Z. Y. Fei, H. J. Gao, and S. Peng, “New results on stabilization of Markovian jump systems with time delay,” Automatica, vol. 45, no. 10, pp. 2300–2306, October 2009.

    Article  MathSciNet  MATH  Google Scholar 

  40. D. Wang, W. Wang, and P. Shi, “Exponential H ∞ filtering for switched linear systems with interval time-varying delay,” International Journal of Robust & Nonlinear Control, vol. 19, no. 5, pp. 532–551, March 2010.

    Article  MathSciNet  MATH  Google Scholar 

  41. D. Zhai, A. Y. Lu, J. H. Li, and Q. L. Zhang, “Simultaneous fault detection and control for switched linear systems with mode-dependentaverage dwell-times,” Applied Mathematics and Computation, vol. 273, pp. 767–792, January 2016.

    Article  MathSciNet  MATH  Google Scholar 

  42. D. Zhai, L. W. An, J. X. Dong, and Q. L. Zhang, “Switched adaptive fuzzy tracking control for a class of switched nonlinear systems under arbitrary switching,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 2, pp. 585–597, April 2018.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Sciences, Northeastern University, Shenyang, Liaoning, 110004, China

    Juan Zhou, Yuanwei Lv, Bo Pang & Cuiping Xue

Authors
  1. Juan Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yuanwei Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bo Pang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Cuiping Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juan Zhou.

Additional information

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

Recommended by Associate Editor Shihua Li under the direction of Editor PooGyeon Park. This work was supported by the Fundamental Research Funds for the Central Universities (N160503004).

Juan Zhou received her Ph.D. degree from Northeastern University in 2014. She is currently a lecturer in Northeastern University. Her research interests are in the areas of singular systems.

Yuanwei Lv is an undergraduate of Northeast University. Her research interests are in the field of control theory.

Bo Pang received her M.Sc. degree in Operational Research and Cybernetics from Northeastern University, in 2016. She is now pursuing a Ph.D. degree in Control Theory and Control Engineering at Northeastern University. Her current research interests focus on T-S fuzzy system, sliding mode control and singular system.

Cuiping Xue received her M.Sc. degree from Northeastern University in 2006. She is currently a lecturer in Northeastern University. Her research interests are in the areas of predictive fault diagnosis.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, J., Lv, Y., Pang, B. et al. H∞ Filtering for a Class of Singular Time-delay Systems. Int. J. Control Autom. Syst. 17, 3131–3139 (2019). https://doi.org/10.1007/s12555-018-0939-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-018-0939-3

Keywords

Search

Navigation