H∞ filtering of two-dimensional T-S fuzzy systems

Circuits, Systems, and Signal Processing

Volumn 33, Issue 6, 2014, Pages 1737-1761

  Boukili, Bensalem ^a   Hmamed, Abdelaziz ^a   Benzaouia, Abdellah ^b   Hajjaji, Ahmed El ^c  

^a SIDI MOHAMED BEN ABDELLAH UNIVERSITY   (Morocco)

^b FACULTÉ DES SCIENCES SEMLALIA   (Morocco)

^c UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

Author keywords

Basis dependent Lyapunov functions; Multidimensional systems; Two dimensional 2D fuzzy systems

Indexed keywords

FUZZY FILTERS; FUZZY SYSTEMS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS;

ASYMPTOTICALLY STABLE; FILTERING PROBLEMS; FORNASINI-MARCHESINI MODEL; LYAPUNOV MATRIX; MULTIDIMENSIONAL SYSTEMS; SYSTEM MATRICES; T S FUZZY SYSTEM; TAKAGI SUGENO FUZZY SYSTEMS;

TWO DIMENSIONAL;

EID: 84902106319     PISSN: 0278081X     EISSN: 15315878     Source Type: Journal    
DOI: 10.1007/s00034-013-9720-2     Document Type: Article

References (38)

1. ∞ filter design for T-S fuzzy systems. IEEE Trans. Fuzzy Syst. 19(4), 770-779 (2011)
2. M. Benhayoun, F. Mesquine, A. Benzaouia, Delay-dependent stabilizability of 2D delayed continuous systems with saturating control. Circuits Syst. Signal Process. (2013). doi: 10.1007/s00034-013-9585-4
3. C.W. Chen, J.S.H. Tsai, L.S. Shieh, Two-dimensional discrete-continuous model conversion. Circuits Syst. Signal Process. 18, 565-585 (1999)
4. J.R. Cui, G.D. Hu, Q. Zhu, Stability and robust stability of 2D discrete stochastic systems. Discrete Dyn. Nat. Soc. 545361, 11 pp. (2011). doi: 10.1155/2011/545361
5. C. De Souza, L. Xie, D. Coutinho, Robust filtering for 2D discrete-time linear systems with convex-bounded parameter uncertainty. Automatica 46(4), 673-681 (2010)
6. ∞ Control and Filtering of Two-dimensional Systems (Springer, Berlin, 2002)
7. ∞ filtering of 2D discrete systems. IEEE Trans. Signal Process. 48(6), 1760-1768 (2000)
8. ∞ filtering of 2D Roesser discrete systems: a polynomial approach. Math. Problems Eng. 521675, 15 pp. (2012)
9. A. Hmamed, A. El Hajjaji, A. Benzaouia, Stabilization of discrete-time 2D T-S fuzzy systems by state feedback control, in 17th Mediterranean Conference on Control and Automation, MED'09, Thessaloniki (2009), pp. 1-6
10. A. Hmamed, F. Mesquine, F. Tadeo, M. Benhayoun, A. Benzaouia, Stabilization of 2D saturated systems by state feedback control. Multidimens. Syst. Signal Process. 21, 277-292 (2010). doi: 10.1007/s11045-010-0107-2
11. A. Hmamed, M. Alfidi, A. Benzaouia, F. Tadeo, LMI conditions for robust stability of 2D linear discrete-time systems. Math. Probl. Eng. 2008, 356124 (2008)
12. A. Hmamed, M. Alfidi, A. Benzaouia, F. Tadeo, Robust stabilisation under linear fractional parametric uncertaines of two-dimensional system with Rosser models. Int. J. Sci. Tech. Autom. Control Comput. Eng. (2007). Special Issue. CSC
13. ∞ filtering for uncertain 2-D continuous systems with delays. Int. J. Innov. Comput. Inf. Control 9(5), 2167-2183 (2013)
14. ∞ control for 2-D discrete nonlinear systems with state delays. Multidimens. Syst. Signal Process. (2013). doi: 10.1007/s11045-013-0230-y
15. S. Huang, Z. Xiang, Delay-dependent stability for discrete 2D switched systems with state delays in the Roesser model. Circuits Syst. Signal Process. (2013). doi: 10.1007/s00034-013-9600-9
16. 2 gain analysis of Takagi-Sugeno fuzzy systems via linear matrix inequalities, in Proceedings of the 14th IFAC Triennial World Congress, (1999), pp. 285-289
17. T. Kaczorek, Two-Dimensional Linear Systems (Springer, Berlin, 1985)
18. ∞ filtering of two-dimensional T-S fuzzy systems. Int. J. Robust Nonlinear Control (2012). doi: 10.1002/rnc.2866
19. ∞ filtering for fuzzy dynamical systems with D stability constraints. IEEE Trans. Circuits Syst. 50(11), 1503-1508 (2003)
20. T. Ooba, On stability analysis of 2D systems based on 2D Lyapunov matrix inequalities. IEEE Trans. Circuits Syst. I 47(8), 1263-1265 (2000)
21. ∞ filtering of 2D discrete state-delayed systems. Multidimens. Syst. Signal Process. 20(3), 265-284 (2009)
22. ∞ filtering for continuous-time polytopic systems with time-varying delay. Int. J. Robust Nonlinear Control 20, 346-365 (2010). doi: 10.1002/rnc.1439
23. T. Tanaka, T. Hori, H.O. Wang, A fuzzy Lyapunov approach to fuzzy control system design, in Proceedings of the American Control Conference, Arlington, V (2001), pp. 4790-4795
24. ∞ filtering of 2D systems. IEEE Trans. Signal Process. 50(7), 1759-1771 (2002)
25. L. Wu, Z. Wang, H. Gao, C. Wang, Filtering for uncertain 2D discrete systems with state delays. Signal Process. 87(9), 2213-2230 (2007)
26. ∞ filtering for 2D Markovian jump systems. Automatica 44(7), 1849-1858 (2008)
27. 1 filtering for two-dimensional linear parameter-varying systems. Int. J. Robust Nonlinear Control 17(12), 1129-1154 (2007)
28. Z. Xiang, S. Huang, Stability analysis and stabilization of discrete-time 2D switched systems. Circuits Syst. Signal Process. 32(1), 401-414 (2013)
29. X. Xie, H. Zhang, Convergent stabilization conditions of discrete-time 2D T-S fuzzy systems via improved homogeneous polynomial techniques. Acta Autom. Sin. 36(9), 1305-1311 (2010)
30. X. Xie, H. Zhang, Stabilization of discrete-time 2D T-S fuzzy systems based on new relaxed conditions. Acta Autom. Sin. 36(2), 267-273 (2010)
31. ∞ filtering for uncertain 2D continuous systems. IEEE Trans. Signal Process. 53(5), 1731-1738 (2005)
32. ∞ filter design for uncertain Takagi-Sugeno fuzzy systems with time delay. J. Eng. Appl. Artif. Intell. 17(6), 645-659 (2004)
33. ∞ filter designs for polytopic two-dimensional systems in Roesser model. Multidimens. Syst. Signal Process. 21(3), 255-275 (2010)
34. F. Yang, Y. Li, Set-membership fuzzy filtering for nonlinear discrete-time systems. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 40(1), 116-124 (2010)
35. ∞ control of two-dimensional systems in Roesser model. Automatica 42(9), 1507-1514 (2006)
36. ∞ filtering of discrete-time fuzzy systems via basis-dependent Lyapunov function approach. Fuzzy Sets Syst. 158(2), 180-193 (2007)
37. ∞ filtering of parameter-varying systems. Int. J. Robust Nonlinear Control 16(8), 397-411 (2006)
38. S. Zhou, T. Li, Robust stabilization for delayed discrete-time fuzzy systems via basis-dependent Lyapunov-Krasovskii function. Fuzzy Sets Syst. 151(1), 139-153 (2005)