Robust stabilization of uncertain descriptor fractional-order systems

Automatica

Volumn 49, Issue 6, 2013, Pages 1907-1913

  N'Doye, Ibrahima ^a   Darouach, Mohamed ^b   Zasadzinski, Michel ^b   Radhy, Nour Eddine ^c  

^a UNIVERSITY OF LUXEMBOURG   (Luxembourg)

^b UNIVERSITÉ DE LORRAINE   (France)

^c FACULTÉ DES SCIENCES AIN CHOCK   (Morocco)

Author keywords

Descriptor fractional order system; Linear matrix inequality (LMI); Normalization; Parameter uncertainty; Robust stabilization; State feedback control

Indexed keywords

FRACTIONAL ORDER; FRACTIONAL-ORDER SYSTEMS; LINEAR MATRIX INEQUALITY FORMULATIONS; NORMALIZATION; NUMERICAL EXAMPLE; PARAMETER UNCERTAINTY; ROBUST STABILIZATION; SUFFICIENT CONDITIONS;

FEEDBACK CONTROL; ROBUST CONTROL; STABILIZATION; STATE FEEDBACK;

LINEAR MATRIX INEQUALITIES;

EID: 84877584640     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2013.02.066     Document Type: Article

References (30)

1. R. Bagley, and R. Calico Fractional order state equations for the control of viscoelastically damped structures Journal of Guidance, Control, and Dynamics 14 1991 304 311
2. S. Boyd, L. El Ghaoui, E. Féron, and V. Balakrishnan Linear matrix inequality in systems and control theory 1994 SIAM Philadelphia
3. A. Bunse-Gerstner, R. Byers, V. Mehrmann, and N. Nichols Feedback design for regularizing descriptor systems Linear Algebra and Its Applications 299 1999 119 151
4. H design with pole placement constraints: an LMI approach IEEE Transactions on Automatic Control 41 1996 358 367
5. M. Chilali, P. Gahinet, and P. Apkarian Robust pole placement in LMI regions IEEE Transactions on Automatic Control 44 1999 2257 2270
6. L. Dai Observers for discrete singular systems IEEE Transactions on Automatic Control 33 1988 187 191
7. L. Dai Singular control systems Lecture notes in control and information sciences vol. 118 1989 Springer-Verlag New York
8. N. Engheta On fractional calculus and fractional multipoles in electromagnetism IEEE Transactions on Antennas and Propagation 44 1996 554 566
9. C. Farges, M. Moze, and J. Sabatier Pseudo-state feedback stabilization of commensurate fractional order systems Automatica 46 2010 1730 1734
10. R. Hilfer Applications of fractional calculus in physics 2001 World Scientific Publishing Singapore
11. H control theory IEEE Transactions on Automatic Control 35 1990 356 361
12. A. Kilbas, H. Srivastava, and J. Trujillo Theory and applications of fractional differential equations North-Holland mathematics studies vol. 204 2006 Elsevier Amsterdam
13. C. Lin, Q. Wang, and T. Lee Robust normalization and stabilization of uncertain descriptor systems with norm-bounded perturbations IEEE Transactions on Automatic Control 50 2005 515 520
14. J. Lu, and Y. Chen Robust stability and stabilization of fractional-order interval systems with the fractional-order the 0 1 case IEEE Transactions on Automatic Control 55 2010 152 158
15. Matignon, D. (1996). Stability results for fractional differential equations with applications to control processing. In Proc. IEEE-IMACS syst. man cyber. conf. Lille, France.
16. Matignon, D. (1998). Generalized fractional differential and difference equations: stability properties and modelling issues. In Proc. mathematical theory of networks and systems symposium. Padova, Italy.
17. N'Doye, I.; Zasadzinski, M.; Darouach, M.; Radhy, N. (2010). Stabilization of singular fractional-order systems: an LMI approach. In Proc. IEEE Mediterranean conf. contr. & aut. Marrakesh, Morocco.
18. D. Peaucelle, D. Arzelier, O. Bachelier, and J. Bernussou A new robust D-stability condition for real convex polytopic uncertainty Systems & Control Letters 40 2000 21 30
19. Petráš, I.; Podlubny, I.; O'Leary, P.; Dorckák, L.; Vinagre, B.M. (2002). Analogue realizations of fractional order controllers. Faculty BERG, TU Košice, Slovakia.
20. I. Podlubny Fractional differential equations 1999 Academic New York
21. I. Podlubny Geometric and physical interpretation of fractional integration and fractional differentiation Fractional Calculus & Applied Analysis 5 2002 367 386
22. Y. Rossikhin, and M. Shitikova Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass system Acta Mechanica 120 1997 109 125
23. Sabatier, J.; Moze, M.; Farges, C. (2008). On stability of fractional order systems. In Proc. IFAC workshop on fractional differentiation and its application. Ankara, Turkey.
24. J. Sabatier, M. Moze, and C. Farges LMI conditions for fractional order systems Computers and Mathematics with Applications 59 2010 1594 1609
25. R. Skelton, T. Iwasaki, and K. Grigoriadis A unified algebraic approach to linear control design 1998 Taylor & Francis London
26. H. Sun, A. Abdelwahad, and B. Onaral Linear approximation of transfer function with a pole of fractional order IEEE Transactions on Automatic Control 29 1984 441 444
27. D. Valério N-integer toolbox 2005 Mathworks Inc
28. B.M. Vinagre, I. Podlubny, A. Hernández, and V. Feliu Some approximations of fractional order operators used in control theory and applications Fractional Calculus & Applied Analysis 3 2000 231 248 Chapter 3
29. H control for linear time-invariant systems with norm-bounded uncertainty in the input matrix Systems & Control Letters 14 1990 389 396
30. S. Xu, C. Yang, Y. Niu, and J. Lam Robust stabilization for uncertain discrete singular systems Automatica 37 2001 769 774