Robust stability analysis and stabilization of fractional order polytopic systems

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 44, Issue 1 PART 1, 2011, Pages 10800-10805

  Farges, Christophe ^a   Sabatier, Jocelyn ^a   Moze, Mathieu ^a  

^a UNIVERSITÉ DE BORDEAUX   (France)

Author keywords

Fractional order systems; Linear Matrix Inequalities; Polytopic systems; Robust control; State feedback

Indexed keywords

CLOSED LOOP SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; LINEAR MATRIX INEQUALITIES; ROBUST CONTROL; ROBUSTNESS (CONTROL SYSTEMS); STABILIZATION; STATE FEEDBACK; UNCERTAINTY ANALYSIS;

FRACTIONAL ORDER; FRACTIONAL-ORDER SYSTEMS; LMI-CONDITION; POLYTOPIC SYSTEM; ROBUST STABILITY ANALYSIS; STABILITY REGIONS; SYSTEM MATRICES; UNCERTAIN PARAMETERS;

SYSTEM STABILITY;

EID: 84866769472     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20110828-6-IT-1002.00779     Document Type: Conference Paper

References (20)

1. Ahn H. S., Chen Y. Q. and I. Podlubny (2007), "Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality," Appl. Math. Comput., vol. 187, no. 1, pp. 27-34
2. Boyd S., El Ghaoui L., Feron E., and Balakrishnan V.(1994) Linear Matrix Inequalities in System and Control Theory. SIAM Studies in Applied Mathematics, Philadelphia.
3. Caputo M. (1967), Linear models of dissipation whose q is almost frequency independent - II. Geophysical Journal International, 13(5):529-539.
4. Chen Y. Q., Ahn H. S. and Podlubny I. (2006), "Robust stability check of fractional order linear time invariant systems with interval uncertainties," Signal Processing, vol. 86 pp. 2611-2618.
5. De Souza C. E. and Trofino A. (2000) An LMI approach to stabilization of linear discrete-time periodic systems. Int. J. Control, 73:696-709.
6. Farges C., Moze M., Sabatier, J. (2010), Pseudo state feedback stabilization of commensurate fractional order systems, Automatica, In Press, http://www.sciencedirect.com/science/article/B6V21-50KMVV7-4/2/ 0b3f2aa00c9ad522b63188facb01fa4d
7. Lofberg J. (2004). Yalmip: A toolbox for modeling and optimizationvin MATLAB. In Proceedings of the CACSD Conference, Taipei, Taiwan
8. Matignon D. (1996), Stability results on fractional differential equations with applications to control processing. In Computational Engineering in Systems Applications, volume 2, pages 963-968, Lille, France.
9. Miller K. S. and Ross B. (1993), An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley & Sons
10. Moze M., Sabatier J. and Oustaloup A. (2005), LMI tools for stability analysis of fractional systems. In 20th ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Technical Conference (ASME IDETC/CIE'05), Long Beach, California, USA.
11. Paucelle D. (2000), Formulation générique de problèmes en analyse et commande robuste par les fonctions de Lyapunov dépendant des paramètres, PhD thesis dissertation, Toulouse III University.
12. Peaucelle D. and Arzelier D. (2000), New LMI-Based Conditions for Robust H2 Performance Analysis. Dans American Control Conference, pages 317-321, Chicago Illinois.
13. Petras I., Chen Y., Vinagre B. M., Podlubny I. (2004), Stability of linear time invariant systems with interval fractional orders and interval coefficients, Proceedings of the International Conference on Computation Cybernetics (ICCC04), Vienna, Austria, 30th August-1st September, pp. 1-4.
14. Petras, I., Stability of fractional order systems with rational orders: A survey, Fractional Calculus and Applied Analysis, vol. 12, no. 3 (2009), 269-298.
15. Sabatier J., Moze M. and Farges C. (2008), On stability of fractional order systems. In Third IFAC workshop on fractional differentiation and its applications FDA'08, Ankara, Turkey.
16. Sabatier J. and C. Farges (2010), On stability of fractional order systems. In Fourth IFAC workshop on fractional differentiation and its applications FDA'10, Badajoz, Spain
17. Samko S. G., Kilbas A. A., and Marichev O. I (1993), Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Science Publishers.
18. Skelton R. E., Iwazaki T. and Grigoriadis K. (1998), A unified approach to linear control design. Taylor and Francis series in Systems and Control.
19. Tan N., Ozguven O. F., and Ozyetkin M. M. (2009), "Robust stability analysis of fractional order interval polynomials," ISA Transactions, vol. 48, no. 2, pp. 166-172
20. Yan W. Y. and Lam J. (2001), On quadratic stability of systems with structured uncertainty, IEEE Trans. Autom. Control, vol. 46, no. 11, pp.1799-1805