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Delay-dependent approach to robust H ∞ filtering for discrete-time singular systems with multiple time-varying delays and polytopic uncertainties

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Abstract

A delay-dependent approach to robust H ∞ filtering is proposed for discrete-time singular systems with multiple time-varying delays and polytopic uncertainties. The delays are interval time-varying delays and uncertainties are a convex compact set of polytopic types. The aim of the designed filter is to guarantee regular, causal, asymptotic stability with H ∞ norm bound of filtering error singular systems. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded lemma (BL) for singular systems with interval time-varying delays is proposed. Based on the result, the existence condition of the robust H ∞ filter and the filter design method are presented in terms of linear matrix inequality (LMI). Finally, two examples are also given to illustrate the effectiveness of the proposed methodology.

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References

  1. A. Elsayed and M. J. Grimble, “A new approach to H ∞ design of optimal linear filters,” IIMA J. Math. Control and Information, vol. 6, pp. 233–251, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  2. X. M. Zhang and Q. L. Han, “Robust H ∞ filtering for a class of uncertain linear systems with time-varying delay,” Automatica, vol. 44, pp. 157–166, 2008.

    Article  MATH  MathSciNet  Google Scholar 

  3. J. C. Geromel and M. C. de Oliveira, “H 2 and H ∞ robust filtering for convex bounded uncertain systems,” IEEE Trans. on Automatic Control, vol. 46, pp. 100–107, 2001.

    Article  MATH  Google Scholar 

  4. R. M. Palhares and P. L. D. Peres, “Robust H ∞ filter design with pole constraints for discrete-time systems,” J. Franklin Institute, vol. 337, pp. 713–723, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  5. H. Gao, J. Lam, L. Xie, and C. Wang, “New approach to mixed H 2/H ∞ filtering for polytopic discrete-time systems,” IEEE Trans. on Signal Processing, vol. 53, pp. 3183–3192, 2005.

    Article  MathSciNet  Google Scholar 

  6. L. Xie, L. Lu, D. Zhang, and H. Zhang, “Improved robust H 2 and H ∞ filtering for uncertain discretetime systems,” Automatica, vol. 40, pp. 873–880, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  7. E. Fridman and U. Shaked, “A new H ∞ filter design for linear time-delay systems,” IEEE Trans. on Signal Processing, vol. 49, pp. 2839–2843, 2001.

    Article  MathSciNet  Google Scholar 

  8. E. Fridman, U. Shaked, and L. Xie, “Robust H ∞ filtering of linear systems with time varying delay,” IEEE Trans. on Automatic Control, vol. 48, pp. 159–165, 2003.

    Article  MathSciNet  Google Scholar 

  9. R. M. Palhares, C. E. de Souza, and P. L. D. Peres, “Robust H ∞ filtering for uncertain discrete-time state-delayed systems,” IEEE Trans. on Signal Processing, vol. 49, pp. 1696–1703, 2001.

    Article  Google Scholar 

  10. H. Gao and C. Wang, “A delay-dependent approach to robust H ∞ filtering for uncertain discrete-time state-delayed systems,” IEEE Trans. on Signal Processing, vol. 52, pp. 1631–1640, 2004.

    Article  MathSciNet  Google Scholar 

  11. J. H. Kim, S. J. Ahn, and S. Ahn, “Guaranteed cost and H ∞ filtering for discrete-time polytopic uncertain systems with time-delay,” J. Franklin Institute, vol. 342, pp. 365–378, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  12. X. M. Zhang and Q. L. Han, “Delay-dependent robust H ∞ filtering for uncertain discrete-time systems with time-varying delay based on a finite sum inequality,” IEEE Trans. on Circuits and Systems-II: Express Briefs, vol. 53, pp. 1466–1470, 2006.

    Article  Google Scholar 

  13. C. E. de Souza, K. A. Barbosa, and M. Fu, “Robust filtering for uncertain linear discrete-time descriptor systems,” Automatica, vol. 44, pp. 792–798, 2008.

    Article  Google Scholar 

  14. I. Masubuchi, Y. Kamitane, A. Ohara, and N. Suda, “H ∞ control for descriptor systems: a matrix inequalities approach,” Automatica, vol. 33, pp. 669–673, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  15. K. Takaba, N. Morihara, and T. Katayama, “A generalized Lyapunov theorem for descriptor system,” Systems and Control Lett., vol. 24, pp. 49–51, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  16. Z. G. Wu and W. N. Zhou, “Delay-dependent robust stabilization for uncertain singular systems with state delay,” Acta Automatica Sinica, vol. 33, pp. 714–718, 2007.

    MATH  MathSciNet  Google Scholar 

  17. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA, 1994.

    MATH  Google Scholar 

  18. S. Xu and J. Lam, “Robust stability and stabilization of discrete singular systems: an equivalent characterization,” IEEE Trans. on Automatic Control, vol. 49, pp. 568–574, 2004.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Electronic Engineering, Sun Moon University, 100, Kalsan-ri, Tangjeong-myeon, Asan-si, Chungnam, 336-708, Korea

    Jong-Hae Kim

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  1. Jong-Hae Kim
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Correspondence to Jong-Hae Kim.

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Recommended by Editorial Board member Duk-Sun Shim under the direction of Editor Young Il Lee.

Jong-Hae Kim received his B.S., M.S., and Ph.D. degrees in Electronics from Kyungpook National University, Korea, in 1993, 1995, and 1998, respectively. He was with STRC at Kyungpook National University from Nov. 1998 to Feb. 2002. He was a research fellow at Osaka University, Japan, for one year from March 2000. Also, he is a visiting scholar at the School of Electrical and Computer Engineering, Georgia Institute of Technology, USA, during the period of January 2010–March 2011. Now, he has been with Sun Moon University since March, 2002. His research interests focus on robust control, robust filtering, signal processing, and industrial application systems.

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Kim, JH. Delay-dependent approach to robust H ∞ filtering for discrete-time singular systems with multiple time-varying delays and polytopic uncertainties. Int. J. Control Autom. Syst. 8, 655–661 (2010). https://doi.org/10.1007/s12555-010-0319-0

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  • DOI: https://doi.org/10.1007/s12555-010-0319-0

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