Skip to main content
SpringerLink
Log in

Reduced-Order \(H_{\infty }\) Filtering with Intermittent Measurements for a Class of 2D Systems

  • Published:
Journal of Control, Automation and Electrical Systems Aims and scope Submit manuscript

Abstract

The problem of \(H_{\infty }\) filter design for a class of 2D systems is solved here in the presence of intermittent measurements. Data dropouts are characterized using a stochastic variable satisfying the Bernoulli random binary distribution. Our attention is focused on the design of reduced-order \(H_{\infty }\) filters such that the filtering error 2D stochastic system is robust mean-square asymptotically stable and fulfills a given \(H_{\infty }\) disturbance attenuation level. We use a new formulation for a class of 2D system Fornasini–Marchesini (FM) models. A sufficient condition is established by means of the linear matrix inequalities (LMI) technique. The efficiency and viability of the proposed techniques and tools are demonstrated through a set of numerical examples.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Benhayoun, M., Mesquine, F., & Benzaouia, A. (2015). Delay-dependent stabilizability of 2D delayed continuous systems with saturating control. Circuits, Systems and Signal Processing, 32(6), 2723–2743. doi:10.1007/s00034-013-9585-4.

    Article  MathSciNet  Google Scholar 

  • Benzaouia, A., Hmamed, A., & Tadeo, F. (2016). Two-dimensional systems: From introduction to state of the art. In Studies in systems, decision and control (Vol. 28). Switzerland: Springer International Publishing. doi:10.1007/978-3-319-20116-0.

  • Boukili, B., Hmamed, A., Benzaouia, A., & El Hajjaji, A. (2014a). \(H_{\infty }\) filtering of two-dimensional T-S fuzzy systems. Circuits, Systems and Signal Processing, 33(6), 1737–1761. doi:10.1007/s00034-013-9720-2.

    Article  MathSciNet  Google Scholar 

  • Boukili, B., Hmamed, A., & Tadeo, F. (2014b). Robust \(H_{\infty }\) filtering of 2D discrete Fornasini–Marchesini systems. International Journal on Sciences and Techniques of Automatic Control & Computer Engineering (IJ-STA), 8(1), 1998–2011.

  • Boukili, B., Hmamed, A., Benzaouia, A., & El Hajjaji, A. (2015). \(H_{\infty }\) state control for 2D fuzzy FM systems with stochastic perturbation. Circuits, Systems and Signal Processing, 34(3), 779–796. doi:10.1007/s00034-014-9889-z.

    Article  MATH  Google Scholar 

  • Boukili, B., Hmamed, A., & Tadeo, F. (2016a). Robust \(H_{\infty }\) filtering for 2-D discrete Roesser systems. Journal of Control, Automation and Electrical Systems. doi:10.1007/s40313-016-0251-5.

  • Boukili, B., Hmamed, A., Zoulagh, T., & Tadeo, F. (2016b). Robust \(H_{\infty }\) filtering for 2D systems with perturbation stochastic. In 5th international conference on systems and control (ICSC) (2016). doi:10.1109/ICoSC.2016.7507029.

  • Bu, X., Wang, H., Hou, Z., & Qian, W. (2014a). \(H_{\infty }\) control for a class of two-dimensional nonlinear systems with intermittent measurements. Applied Mathematics and Computation, 247, 651–662.

    Article  MathSciNet  MATH  Google Scholar 

  • Bu, X., Wang, H., Hou, Z., & Qian, W. (2014b). Stabilisation of a class of two-dimensional nonlinear systems with intermittent measurements. IET Control Theory and Applications, 8(15), 1596–1604. doi:10.1049/iet-cta.2014.0170.

  • Cui, J., & Hu, G. (2010). State estimation of 2-D stochastic systems represented by FM-II model. Acta Automatica Sinica, 36(5), 755–761.

    MathSciNet  Google Scholar 

  • Cui, J. R., Hu, G. D., & Zhu, Q. (2011). Stability and robust stability of 2D discrete stochastic systems. Discrete Dynamics in Nature and Society, 2011(2011). doi:10.1155/2011/545361.

  • Dai, J., Guo, Z., & Wang, S. (2013). Robust \(H_{\infty }\) control for a class of 2-D nonlinear discrete stochastic systems. Circuits, Systems and Signal Processing, 32(5), 2297–2316. doi:10.1007/s00034-013-9573-8.

    Article  MathSciNet  Google Scholar 

  • De Souza, C., Xie, L., & Coutinho, D. (2010). Robust filtering for 2D discrete-time linear systems with convex-bounded parameter uncertainty. Automatica, 46(4), 673–681.

    Article  MathSciNet  MATH  Google Scholar 

  • Duan, Z., & Xiang, Z. (2014). Output feedback \(H_{\infty }\) stabilization of 2D discrete switched systems in FM LSS model. Circuits, Systems and Signal Processing, 33, 1095. doi:10.1007/s00034-013-9680-6.

    Article  MathSciNet  Google Scholar 

  • Duan, Z., Xiang, Z., & Karimi, H. R. (2013). Delay-dependent \(H_{\infty }\) control for 2-D switched delay systems in the second FM model. Journal of the Franklin Institute, 350(7), 16971718.

    Article  MathSciNet  Google Scholar 

  • Duan, Z., Xiang, Z., & Karimi, H. R. (2014). Robust stabilisation of 2D state-delayed stochastic systems with randomly occurring uncertainties and nonlinearities. International Journal of Systems Science, 45(7), 1402–1415.

    Article  MathSciNet  MATH  Google Scholar 

  • Du, C., & Xie, L. (2002). \(H_{\infty }\) control and filtering of two-dimensional systems. Berlin: Springer.

  • El-Kasri, C., Hmamed, A., Alvarez, T., & Tadeo, F. (2012). Robust \(H_{\infty }\) filtering of 2D Roesser discrete systems: A polynomial approach. Mathematical Problems in Engineering, 2012, Article ID 521675, p. 15.

  • El-Kasri, C., Hmamed, A., & Tadeo, F. (2013a). Reduced-Order \(H_{\infty }\) filters for uncertain 2-D continuous systems, via LMIs and polynomial matrices. Circuits, Systems, and Signal Processing, 33(4), 1189–1214. doi:10.1007/s00034-013-9689-x.

    Article  MathSciNet  Google Scholar 

  • El-Kasri, C., Hmamed, A., Tissir, E. H., & Tadeo, F. (2013b). Robust \(H_{\infty }\) filtering for uncertain two-dimensional continuous systems with time-varying delays. Multidimensional Systems and Signal Processing, 24(4), 685–706.

    Article  MathSciNet  MATH  Google Scholar 

  • Feng, J., & Han, K. (2015). Robust full- and reduced-order energy-to-peak filtering for discrete-time uncertain linear systems. Signal Processing, 108, 183–194.

    Article  Google Scholar 

  • Gao, H., Lam, J., Wang, C., & Xu, S. (2004). Robust \(H_{\infty }\) filtering for 2-D stochastic systems. Circuits, Systems and Signal Processing, 23(6), 479–505.

  • Gao, H., Meng, X., & Chen, T. (2008). New design of Robust \(H_{\infty }\) filters for 2-D systems. IEEE Signal Processing Letters, 15, 217–220.

    Article  Google Scholar 

  • Gao, H., Zhao, Y., & Lam, J. (2009). \(H_{\infty }\) fuzzy filtering of nonlinear systems with intermittent measurements. IEEE Transactions on Fuzzy Systems, 17(2), 291–299.

    Article  Google Scholar 

  • Hmamed, A., Kasri, C. E., Tissir, E. H., Alvarez, T., & Tadeo, F. (2013). Robust \(H_{\infty }\) filtering for uncertain 2-D continuous systems with delays. International Journal of Innovative Computing, Information and Control, 9(5), 2167–2183.

    MATH  Google Scholar 

  • Kririm, S., Hmamed, A., & Tadeo, F. (2015). Robust \(H_{\infty }\) filtering for uncertain 2D singular Roesser models. Circuits, Systems and Signal Processing, 34(7), 2213–2235.

    Article  MathSciNet  MATH  Google Scholar 

  • Li, X., & Gao, H. (2012a). Generalized Kalman-Yakubovich-Popov lemma for 2-D FM LSS model and its application to finite frequency positive real control. IEEE Transactions on Signal Processing, 57(12), 3090–3103.

    Google Scholar 

  • Li, X., & Gao, H. (2012b). Robust finite frequency \(H_{\infty }\) filtering for uncertain 2-D Roesser systems. Automatica, 48, 1163–1170.

    Article  MathSciNet  MATH  Google Scholar 

  • Li, X., & Gao, H. (2013). Robust finite frequency image filtering for uncertain 2-D systems: The FM model case. Automatica, 29(8), 2446–2452.

    Article  Google Scholar 

  • Li, X., & Gao, H. (2014). Reduced-order generalized \(H_{\infty }\) filtering for linear discrete—Time systems with application to channel equalization. IEEE Transactions on Signal Processing, 62(13), 3393–3402.

    Article  MathSciNet  Google Scholar 

  • Li, X., Wang, W., & Li, L. (2013). \(H_{\infty }\) control for 2-D T-S fuzzy FMII model with stochastic perturbation. International Journal of Systems Science,. doi:10.1080/00207721.2013.793780.

    MATH  Google Scholar 

  • Liu, X., Gao, H., & Shi, P. (2009). Robust \(H_{\infty }\) filtering for 2-D systems with intermittent measurements. Circuits, Systems and Signal Processing, 28, 283–303. doi:10.1007/s00034-008-9081-4.

    Article  MathSciNet  MATH  Google Scholar 

  • Qiu, J., Feng, G., & Yang, J. (2010). A new design of delay-dependent robust \(H_{\infty }\) filtering for continuous-time polytopic systems with time-varying delay. International Journal of Robust and Nonlinear Control, 20, 346–365. doi:10.1002/rnc.1439.

    Article  MathSciNet  MATH  Google Scholar 

  • Shi, P., Luan, X., & Lui, F. (2012). \(H_{\infty }\) filtering for discrete-time systems with stochastic incomplete measurement and mixed delays. IEEE Transactions on Industrial Electronics, 59(6), 2732–2738.

    Article  Google Scholar 

  • Tuan, H. D., Apkarian, P., Nguyen, T. Q., & Narikiyo, T. (2002). Robust mixed \(H_{2}/H_{\infty }\) filtering for 2-D systems. IEEE Transactions on Signal Processing, 50(7), 1759–1771.

    Article  Google Scholar 

  • Wang, L., & Liu, X. (2013). \(H_{\infty }\) filtering design for 2-D discrete-Time linear systems with polytopic uncertainty. Circuits, Systems and Signal Processing, 32(1), 333–345. doi:10.1007/s00034-012-9436-8.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Faculty of Sciences Dhar El Mehraz, University of Sidi Mohamed Ben Abdellah, B.P. 1796, Fes-Atlas, Morocco

    Bensalem Boukili & Abdelaziz Hmamed

  2. Department of Systems Engineering and Automatic Control, University of Valladolid, 47005, Valladolid, Spain

    Fernando Tadeo

Authors
  1. Bensalem Boukili
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdelaziz Hmamed
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fernando Tadeo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bensalem Boukili.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Boukili, B., Hmamed, A. & Tadeo, F. Reduced-Order \(H_{\infty }\) Filtering with Intermittent Measurements for a Class of 2D Systems. J Control Autom Electr Syst 27, 597–607 (2016). https://doi.org/10.1007/s40313-016-0271-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40313-016-0271-1

Keywords

Search

Navigation