Stabilization of discrete-time 2D T-S fuzzy systems by state feedback control

2009 17th Mediterranean Conference on Control and Automation, MED 2009

Volumn , Issue , 2009, Pages 1-6

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

^a SIDI MOHAMED BEN ABDELLAH UNIVERSITY   (Morocco)

^b UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

^c FACULTÉ DES SCIENCES SEMLALIA   (Morocco)

Author keywords

2D systems; LMI's; Multiple lyapunov functions; Nonlinear systems; Stabilizability; Takagi sugeno fuzzy model

Indexed keywords

2-D SYSTEMS; LMI'S; MULTIPLE LYAPUNOV FUNCTION; STABILIZABILITY; TAKAGI SUGENO FUZZY MODELS;

ASYMPTOTIC STABILITY; CONTINUOUS TIME SYSTEMS; CONTROL SYSTEM STABILITY; DIFFERENTIAL EQUATIONS; DISCRETE TIME CONTROL SYSTEMS; FEEDBACK CONTROL; FUZZY SYSTEMS; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; NONLINEAR SYSTEMS; STATE FEEDBACK;

FEEDBACK;

EID: 70449808518     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/MED.2009.5164505     Document Type: Conference Paper

References (25)

1. A. Benzaouia, D. Mehdi, A. El Hajjaji and M. Nachidi, Piecewise Quadratic Lyapunov Function for Nonlinear Systems with Fuzzy Static Output Feedback Control. European Control Conference, Kos, Greece, 2-5 July 2007.
2. Brian D. O. Anderson, P. Agathoklis, E. I. Jury and M. Mansour,.Stability and the Matrix Lyapunov Equation for Discrete 2- Dimensional Systems,.IEEE Trans. Circuits Syst., vol. CAS-33, pp. 261-266, Mar. 1986.
3. M. Chadli, D. Maquin and J. Ragot. An LMI formulation for output feedback stabilization in multiple model approach. In Proc. of the 41 th CDC, Las Vegas, Nevada, 2002.
4. A. El Hajjaji, A. Ciocan, and D. Hamad, Four wheel steering control by fuzzy approach, Int. Conf. on AI, Simulation and planning in high autonomy systems (Lisbone, Portugal), no. 44, 2002, pp. 227-231.
5. A.El Hajjaji, A. Benzaouia and M. Naib, Stabilization of fuzzy systems with constrained controls by using positively invariant sets, Mathematical Problems in Engineering, Vo. 2006, Article ID 13832, Pages 117, 2006.
6. T. M. Guerra and L. Vermeiren, LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form, Automatica, Vol. 40, No., pp.823-829, 2004.
7. G. Feng. Stability analysis of discrete-time fuzzy dunamic systems based on piecewise lyapunov functions. IEEE Trans. Fuzzy Syst., Vol:12;No 1; pp: 22-28, 2004.
8. E. Fornasini and G. Marchesini,.Doubly-indexed dynamical systems: state-space models and structural properties,. Math. Syst. Theory, vol. 12, pp. 59-72, 1978.
9. D. D. Givone and R. P. Roesser,.Multidimentional linear iterative circuits-General properties,. IEEE Trans. comp., vol. 21 (10), pp. 1067-1073, 1972.
10. E. Fornasini and G. Marchesini,.State-space realization theory of twodimentional -lters,. IEEE Trans. Aut. Contr., vol. 21 (4), pp. 484-492, 1976.
11. K. Galkowski, E. Rogers, S. Xu, J. Lam and D. H. Owens.LMIs-A Fundamental Tool in Analysis and Controller Design for Discrete Linear Repetitive Process,.IEEE Trans. circuits and syst., Vol. 49, No.6, pp. 768-778, Jun. 2002.
12. A. Hmamed, M. Alfidi, A. Benzaouia, and F. Tadeo, LMI Conditions for Robust Stability of 2D Linear Discrete-Time Systems, Mathematical Problems in Engineering, Vo. 2008, Article ID 356124, 11 pages, 2008.
13. T. Kaczorek,.Realization problem, reachability and minimum energy control of positive 2D Roesser model,. In Proc. 6th Ann. Int. conf. Advances in communication and control, 1997, pp. 765-776.
14. W-S. Lu,.Some New Results on Stability Robustness of Two- Dimensional Discrete Systems,.Multidimensional Syst. and Signal Proc. Vol. 5, pp. 345-361, 1994.
15. E. B. Lee and W-S. Lu,.Stabilization of Two-Dimensional Systems,.IEEE Trans. Automatic Control, Vol. AC-30, pp. 409-411, Apr. 1985.
16. E. Yaz,.On State-feedback Stabilization of Two-Dimensional digital Systems,.IEEE Trans. circuits and syst., Vol. CAS-32, pp. 1069-1070, Oct. 1985.
17. W. Marszalek,.Two dimensional state-space discrete models for hyperbolic partial differential equations., Appl. Math. Models, vol. 8, pp. 11-14, 1984.
18. M. Nachidi, F. Tadeo, A. Hmamed and A. Benzaouia, Static outputfeedback stabilization for time-delay Takagi-Sugeno fuzzy systems, Proc. of the 46 th CDC, New Orleans, 2007.
19. M. Nachidi, A. Benzaouia, F. Tadeo and M. Ait Rami, LMI-based approach for output feedback stabilization for discrete-time Takagi- Sugeno systems, IEEE Trans. Fuzzy Syst. To appear, 2008.
20. T. Takagi and M. Sugeno, Fuzzy identi-cation of systems and its applications to modeling and control, IEEE Trans. Syst., Man, Cybern. 15, no. 9, 116132, 1985.
21. M. Johansson, A. Rantzer and K. Arzen. Piecewise quadratic stability of fuzzy systems. IEEE Trans. Fuzzy Syst., V ol:7;No 6; pp: 713-722, 1999.
22. R. Roesser,.A discrete state-space model for linear image processing,. IEEE Trans. Automat. Contr., vol. AC-20. pp.1-10, Jan. 1975.
23. K. Tanaka, T. Hori and H. O. Wang, A multiple Lyapunov function approach to stabilization of fuzzy control systems, IEEE Trans. Fuzzy Syst. Vol. 11, No. 4, pp. 582-589, 2003.
24. H. O. Wang, K. Tanaka, and M. F. Griffn, An approach to fuzzy control of nonlinear systems: Stability and design issues, IEEE Trans. Fuzzy Syst. 4 (1996), no. 1, 1423.
25. L. Wu-sheng and E. B. Lee,.Stability analysis for two-dimensional systems via a Lyapunov Approach,. IEEE Trans. Circuits Syst., vol. CAS-32, pp. 61-68. Jan. 1985.