Robust stability analysis for a class of fractional order systems with uncertain parameters

Journal of the Franklin Institute

Volumn 348, Issue 6, 2011, Pages 1101-1113

  Liao, Zeng ^a   Peng, Cheng ^a   Li, Wang ^a   Wang, Yong ^a  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTICAL STABILITY; FRACTIONAL ORDER; FRACTIONAL-ORDER SYSTEMS; ILLUSTRATIVE EXAMPLES; INTERVAL SYSTEMS; LINEAR COUPLING; LINEAR TIME-INVARIANT; MODEL PARAMETERS; ROBUST STABILITY; ROBUST STABILITY ANALYSIS; UNCERTAIN PARAMETERS;

LINEAR MATRIX INEQUALITIES; UNCERTAINTY ANALYSIS;

SYSTEM STABILITY;

EID: 79957607884     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfranklin.2011.04.012     Document Type: Article

References (31)

1. P.J. Torvik, and R.L. Bagley On the appearance of the fractional derivative in the behavior of real materials Journal of Applied Mechanics 51 2 1984 294 298 (Pubitemid 14583152)
2. J.J. de Espíndola, C.A. Bavastri, and E.M.O. Lopes On the passive control of vibrations with viscoelastic dynamic absorbers of ordinary and pendulum types Journal of the Franklin Institute 347 1 2010 102 115
3. X. Wu, J. Li, and G. Chen Chaos in the fractional order unified system and its synchronization Journal of the Franklin Institute 345 4 2008 392 401
4. α) Journal of the Franklin Institute 347 10 2010 1797 1813
5. A. Carpinteri, and F. Mainardi Fractals and fractional calculus in continuum mechanics 1997 Springer Wien
6. C.X. Zhu, and Y. Zou Summary of research on fractional-order control Control and Decision 24 2 2009 161 169
7. I. Podlubny Fractional Differential Equations, Mathematics in Science and Engineering 1999 Academic Press New York
8. C.M. Monje, Y.Q. Chen, B.M. Vinagre, D. Xue, and V. Feliu Fractional-order Systems and Controls - Fundamentals and Applications, Advanced Industrial Control Series 2010 Springer-Verlag London
9. H. Sheng, Y. Li, and Y.Q. Chen Application of numerical inverse Laplace transform algorithms in fractional calculus Journal of the Franklin Institute 348 2 2011 315 330
10. Y. Çenesiz, Y. Keskin, and A. Kurnaz The solution of the BagleyTorvik equation with the generalized Taylor collocation method Journal of the Franklin Institute 347 2 2010 452 466
11. μ-controllers IEEE Transactions on Automatic Control 44 1 1999 208 214
12. I. Podlubny, I. Petráš, B.M. Vinagre, P. OLeary, and L. Dorčák Analogue realizations of fractional-order controllers Nonlinear Dynamics 29 2002 281 296 (Pubitemid 34945402)
13. D. Matignon, Stability result on fractional differential equations with applications to control processing, in: Proceedings of the IMACS-SMC, Lille, France, 1996, 963968.
14. D. Matignon, Stability properties for generalized fractional differential systems, in: Proceedings of the Colloquium FDS98: Fractional Differential Systems: Models, Methods and Applications, vol. 5, Paris, 1998, pp. 145158.
15. D. Matignon, Generalized fractional differential and difference equations: stability properties and modeling issues, in: Proceedings of the Mathematical Theory of Networks and Systems symposium (MTNS98), Padova, Italy, July 1998, 503506.
16. A. Oustaloup, P. Melchior, The great principles of the CRONE control, in: Proceedings of the Systems, Man and Cybernetics. Systems Engineering in the Service of Humans, 1993, 118129.
17. A. Oustaloup, M. Bansard, First generation CRONE control, in: Proceedings of the Systems, Man and Cybernetics. Systems Engineering in the Service of Humans, 1993, 130135.
18. A. Oustaloup, B. Mathieu, P. Lanusse, Second generation CRONE control, in: Proceedings of the Systems, Man and Cybernetics. Systems Engineering in the Service of Humans, 1993, 136142.
19. A. Oustaloup, B. Bluteau, M. Nouillant, First generation scalar CRONE control: application to a two DOF manipulator and comparison with non linear decoupling control, in: Proceedings of the Systems, Man and Cybernetics. Systems Engineering in the Service of Humans, 1993, 453458.
20. B.M. Vinagre, Y.Q. Chen, and I. Petráš Two direct Tustin discretization methods for fractional-order differentiator/integrator Journal of the Franklin Institute 340 5 2003 349 362
21. Z.B. Wang, G.Y. Cao, and X.J. Zhu Stability conditions and criteria for fractional order linear time-invariant systems Control Theory & Applications 21 6 2004 922 926
22. Z.B. Wang, G.Y. Cao, and X.J. Zhu Research on the internal and external stability of fractional order linear systems Control and Decision 19 10 2004 1171 1174
23. J.B. Hu, Y. Han, and L.D. Zhao A novel stability theorem for fractional systems and its applying in synchronizing fractional chaotic system based on back-stepping approach Acta Physica Sinica 58 4 2009 2235 2239
24. Y.Q. Chen, and K.L. Moore Analytical stability bound for delayed second-order systems with repeating poles using Lambert function W Automatica 38 5 2002 891 895 (Pubitemid 34201133)
25. M. Moze, J. Sabatier, A. Oustaloup, LMI tools for stability analysis of fractional systems, in: Proceedings of the International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, California, USA, 2005, pp. 16111619. (Pubitemid 43274678)
26. J. Sabatier, M. Moze, and C. Farges LMI stability conditions for fractional order systems Computers & Mathematics with Applications 59 5 2010 1594 1609
27. H.S. Ahn, Y.Q. Chen, and I. Podlubny Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality Applied Mathematics and Computation 187 1 2007 27 34 (Pubitemid 46656399)
28. Y.Q. Chen, H.S. Ahn, and I. Podlubny Robust stability check of fractional order linear time invariant systems with interval uncertainties Signal Processing 86 10 2006 2611 2618 (Pubitemid 44026624)
29. H.S. Ahn, and Y.Q. Chen Necessary and sufficient stability condition of fractional-order interval linear systems Automatica 44 11 2008 2985 2988
30. J.G. Lu, and G.R. Chen Robust stability and stabilization of fractional-order interval systems: an LMI approach IEEE Transactions on Automatic Control 54 6 2009 1294 1299
31. J.G. Lu, and Y.Q. Chen Robust stability and stabilization of fractional-order interval systems with the fractional order α: the 0<α<1 case IEEE Transactions on Automatic Control 55 1 2010 152 158