231
Views
15
CrossRef citations to date
0
Altmetric
Articles

Filter design for discrete-time two-dimensional T–S fuzzy systems with finite frequency specification

, ORCID Icon &
Pages 599-613 | Received 13 Nov 2017, Accepted 17 Dec 2018, Published online: 07 Jan 2019

References

  • Bachelier, O., Paszke, W., & Mehdi, D. (2018). On the KYP lemma and the multidimensional models. Multidimensional Systems and Signal Processing, 19, 425–447. doi: 10.1007/s11045-008-0055-2
  • Cao, S., Rees, N., & Feng, G. (1997). Analysis and design for a class of complex control systems. Part I: Fuzzy modeling and identification. Automatica, 33, 1017–1028. doi: 10.1016/S0005-1098(97)00010-1
  • Chen, X., Lam, J., Gao, H., & Zhou, S. (2013). Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions. Multidimensional Systems and Signal Processing, 24, 395–415. doi: 10.1007/s11045-011-0166-z
  • Chen, Y., Zhang, W., & Gao, H. (2010). Finite frequency H∞ control for building under earthquake excitation. Mechatronics, 20, 128–142. doi: 10.1016/j.mechatronics.2009.11.001
  • Dey, A., & Kar, H. (2011). Robust stability of 2-D discrete systems employing generalized overflow nonlinearities: An LMI approach. Digital Signal Processing, 21, 262–269. doi: 10.1016/j.dsp.2010.06.010
  • Ding, D. W., Li, X. J., Du, X. D. X., & Xie, X. (2016). Finite-frequency model reduction of Takagi–Sugeno fuzzy systems. IEEE Transactions on Fuzzy Systems, 24, 1464–1474. doi: 10.1109/TFUZZ.2016.2540060
  • Ding, D. W., & Yang, G. H. (2010). Fuzzy filter design for nonlinear systems in finite-frequency domain. IEEE Transactions on Fuzzy Systems, 18, 935–945. doi: 10.1109/TFUZZ.2010.2058807
  • Du, C., & Xie, L. (2002). H control and filtering of two-dimensional systems. Berlin: Springer-Verlag.
  • Du, C., Xie, L., & Zhang, C. (2001). H∞ control and robust stabilization of two-dimensional systems in Roesser models. Automatica, 37, 205–211. doi: 10.1016/S0005-1098(00)00155-2
  • Duan, Z., Xiang, Z., & Karimi, H. (2014a). Robust stabilization of 2D state-delayed stochastic systems with randomly occurring uncertainties and nonlinearities. International Journal of Systems Science, 45, 1402–1415. doi: 10.1080/00207721.2013.835004
  • Duan, Z., Xiang, Z., & Karimi, H. (2014b). Stability and l1-gain analysis for positive 2-D T–S fuzzy state-delayed systems in the second FM model. Neurocomputing, 142, 209–215. doi: 10.1016/j.neucom.2014.04.047
  • Elsayed, A., & Grimble, M. (1989). A new approach to the H∞ design of optimal digital linear filters. IMA Journal of Mathematical Control and Information, 6, 233–251. doi: 10.1093/imamci/6.2.233
  • Gahinet, P., & Apkarian, P. (1994). A linear matrix inequality approach to H∞ control. International Journal of Robust and Nonlinear Control, 4, 421–448. doi: 10.1002/rnc.4590040403
  • Gao, H., & Li, X. (2011). H∞ filtering for discrete-time state-delayed systems with finite frequency specifications. IEEE Transactions on Automatic Control, 56, 2935–2941. doi: 10.1109/TAC.2011.2159909
  • Gao, H., & Li, X. (2014). Robust filtering for uncertain systems: A parameter-dependent approach. Cham: Springer Science & Business Media.
  • Hinamoto, T. (2001). Stability of 2-D discrete systems described by the Fornasini–Marchesini second model. IEEE Transactions on Circuits & Systems I: Fundamental Theory & Applications, 44, 254–257. doi: 10.1109/81.557373
  • Hu, G., & Liu, M. (2005). Simple criteria for stability of two-dimensional linear systems. IEEE Transactions on Signal Processing, 53, 4720–4723. doi: 10.1109/TSP.2005.859265
  • Iwasaki, T., & Hara, S. (2005). Generalized KYP lemma: Unified frequency domain inequalities with design applications. IEEE Transactions on Automatic Control, 50, 41–59. doi: 10.1109/TAC.2004.840475
  • Iwasaki, T., Hara, S., & Fradkov, A. (2005). Time domain interpretations of frequency domain inequalities on (semi)finite ranges. Systems & Control Letters, 54, 681–691. doi: 10.1016/j.sysconle.2004.11.007
  • Kaczorek, T. (1985). Two-dimensional linear systems. Berlin:Springer-Verlag.
  • Lacerda, M., Oliveira, R., & Peres, P. (2011). Robust H2 and H∞ filter design for uncertain linear systems via LMIs and polynomial matrices. Signal Processing, 91, 1115–1122. doi: 10.1016/j.sigpro.2010.10.013
  • Li, X., & Gao, H. (2012). Robust finite frequency H∞ filtering for uncertain 2-D Roesser systems. Automatica, 48, 1163–1170. doi: 10.1016/j.automatica.2012.03.012
  • Li, X., & Gao, H. (2013). Robust finite frequency H∞ filtering for uncertain 2-D systems: The FM model case. Automatica, 49, 2446–2452. doi: 10.1016/j.automatica.2013.04.014
  • Li, X., Gao, H., & Wang, C. (2012). Generalized Kalman–Yakubovich–Popov lemma for 2-D FM LSS model. IEEE Transactions on Automatic Control, 57, 3090–3103. doi: 10.1109/TAC.2012.2200370
  • Li, L., & Wang, W. (2012). Fuzzy modeling and H∞ control for general 2-D nonlinear systems. Fuzzy Sets & Systems, 207, 1–26. doi: 10.1016/j.fss.2012.04.002
  • Li, L., Wang, W., & Li, X. (2013). New approach to H∞ filtering of two-dimensional T–S fuzzy systems. International Journal of Robust and Nonlinear Control, 23, 1990–2012. doi: 10.1002/rnc.2866
  • Li, X., Wang, W., & Li, L. (2015). H∞ control for 2-D T–S fuzzy FMII model with stochastic perturbation. International Journal of Systems Science, 46, 609–624. doi: 10.1080/00207721.2013.793780
  • Li, X. J., & Yang, G. H. (2017). Finite frequency L2–L∞ filtering of T–S fuzzy systems with unknown membership functions. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 47, 1884–1897. doi: 10.1109/TSMC.2016.2563390
  • Luo, Y., Wang, Z., Liang, J., Wei, G., & Alsaadi, F. E. (2017). H∞ control for 2-D fuzzy systems with interval time-varying delays and missing measurements. IEEE Transactions on Cybernetics, 47, 365–377. doi: 10.1109/TCYB.2016.2623859
  • Mamdani, E. (1974). Application of fuzzy algorithms for control of simple dynamic plant. Proceedings of the Institution of Electrical Engineers, 121, 1585–1588. doi: 10.1049/piee.1974.0328
  • Marszalek, W. (1984). Two-dimensional state-space discrete models for hyperbolic partial differential equations. Applied Mathematical Modelling, 8, 11–14. doi: 10.1016/0307-904X(84)90170-7
  • Precup, R., & Hellendoorn, H. (2011). A survey on industrial applications of fuzzy control. Computers in Industry, 62, 213–226. doi: 10.1016/j.compind.2010.10.001
  • Ren, Y., Ding, D. W., & Li, Q. (2017). Finite-frequency fault detection for two-dimensional Fornasini–Marchesini dynamical systems. International Journal of Systems Science, 48, 2610–2621. doi: 10.1080/00207721.2017.1333169
  • Rubio, F., Berenguel, M., & Camacho, E. (1995). Fuzzy logic control of a solar power plant. IEEE Transactions on Fuzzy Systems, 3, 459–468. doi: 10.1109/91.481955
  • Shaker, H., & Tahavori, M. (2010). Stability analysis for a class of discrete-time two-dimensional nonlinear systems. Multidimensional Systems and Signal Processing, 21, 293–299. doi: 10.1007/s11045-010-0106-3
  • Singh, V. (2012). New approach to stability of 2-D discrete systems with state saturation. Signal Processing, 92, 240–247. doi: 10.1016/j.sigpro.2011.07.012
  • Sun, W. C., Zhao, Y., Li, J. F., Zhang, L. X., & Gao, H. J. (2012). Active suspension control with frequency band constraints and actuator input delay. IEEE Transactions on Industrial Electronics, 59, 530–537. doi: 10.1109/TIE.2012.2183837
  • Takaba, K., & Katayama, T. (1996). Discrete-time H∞ algebraic Riccati equation and parametrization of all H∞ filters. International Journal of Control, 64, 1129–1149. doi: 10.1080/00207179608921678
  • Wang, L., Chen, W., & Li, L. (2017). Dissipative stability analysis and control of two-dimensional Fornasini–Marchesini local state–space model. International Journal of Systems Science, 48, 1744–1751. doi: 10.1080/00207721.2017.1282059
  • Wang, L., Wang, W., Gao, J., & Chen, W. (2017). Stability and robust stabilization of 2-D continuous-discrete systems in Roesser model based on KYP lemma. Multidimensional Systems & Signal Processing, 28, 1–14. doi: 10.1007/s11045-015-0326-7
  • Wang, H., & Yang, G. H. (2016). H∞ controller design for affine fuzzy systems based on piecewise Lyapunov functions in finite-frequency domain. Fuzzy Sets and Systems, 290, 22–38. doi: 10.1016/j.fss.2015.06.013
  • Xiao, J., Xiao, J., Xi, N., Tummala, R. L., & Mukherjee, R. (2004). Fuzzy controller for wall-climbing microrobots. IEEE Transactions on Fuzzy Systems, 12, 466–480. doi: 10.1109/TFUZZ.2004.832520
  • Xie, X., & Zhang, H. (2010). Stabilization of discrete-time 2-D T–S fuzzy systems based on new relaxed conditions. Acta Automatica Sinica, 36, 267–273.
  • Xu, S., & Chen, T. (2002). Reduced-order H∞ filtering for stochastic systems. IEEE Transactions on Signal Processing, 50, 2998–3007. doi: 10.1109/TSP.2002.805239
  • Xu, S., & Lam, J. (2007). Reduced-order H∞ filtering for singular systems. Systems & Control Letters, 56, 48–57. doi: 10.1016/j.sysconle.2006.07.010
  • Xu, H., Zou, Y., Lu, J., & Xu, S. (2005). Robust H∞ control for a class of uncertain nonlinear two-dimensional systems with state delays. Journal of the Franklin Institute, 342, 877–891. doi: 10.1016/j.jfranklin.2005.07.003
  • Yang, R. H., & Lim, Y. C. (2002). A dynamic frequency grid allocation scheme for the efficient design of equiripple FIR filters. IEEE Transactions on Signal Processing, 44, 2335–2339. doi: 10.1109/78.536689
  • Yang, H., Xia, Y., & Liu, B. (2011). Fault detection for T–S fuzzy discrete systems in finite-frequency domain. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 41, 911–920. doi: 10.1109/TSMCB.2010.2099653
  • Yang, R., Xie, L., & Zhang, C. (2008). Generalized two-dimensional Kalman–Yakubovich–Popov lemma for discrete Roesser model. IEEE Transactions on Circuits and Systems I: Regular Papers, 55, 3223–3233. doi: 10.1109/TCSI.2008.923284
  • Zhou, K., Doyle, J. C., & Glover, N. (1996). Robust and optimal control. Upper Saddle River, NJ: Prentice Hall.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.